Intuition

Intuition is the ability to acquire knowledge without recourse to conscious reasoning. Different fields use the word "intuition" in very different ways, including but not limited to: direct access to unconscious knowledge; unconscious cognition; inner sensing; inner insight to unconscious pattern-recognition; and the ability to understand something instinctively, without any need for conscious reasoning.
The word "intuition" comes from the Latin verb "intueri" translated as "consider" or from the late middle English word "intuit", "to contemplate".
Philosophy.
Both Eastern and Western philosophers have studied the concept in great detail. Philosophy of mind deals with the concept.
Eastern philosophy.
In the East intuition is mostly intertwined with religion and spirituality, and various meanings exist from different religious texts.
Hinduism.
In Hinduism various attempts have been made to interpret the Vedic and other esoteric texts.
For Sri Aurobindo, intuition comes under the realms of knowledge by identity; he describes the psychological plane in humans (often referred to as mana in Sanskrit) having two arbitrary natures, the first being imprinting of psychological experiences which is constructed through sensory information (mind seeking to become aware of external world). The second nature being the action when it seeks to be aware of itself, resulting in humans being aware of their existence or aware of being angry & aware of other emotions. He terms this second nature as knowledge by identity.
He finds that at present as the result of evolution the mind has accustomed itself to depend upon certain physiological functioning and their reactions as its normal means of entering into relations with the outer material world. As a result, when we seek to know about the external world the dominant habit is through arriving at truths about things via what our senses convey to us. However, knowledge by identity, which we currently only give the awareness of human beings' existence, can be extended further to outside of ourselves resulting in intuitive knowledge.
He finds this intuitive knowledge was common to older humans (Vedic) and later was taken over by reason which currently organises our perception, thoughts and actions resulting from Vedic to metaphysical philosophy and later to experimental science. He finds that this process, which seems to be decent, is actually a circle of progress, as a lower faculty is being pushed to take up as much from a higher way of working. He finds when self-awareness in the mind is applied to one's self and the outer (other) -self, results in luminous self-manifesting identity; the reason also converts itself into the form of the self-luminous intuitional knowledge.
Osho believed consciousness of human beings to be in increasing order from basic animal instincts to intelligence and intuition, and humans being constantly living in that conscious state often moving between these states depending on their affinity. He also suggests living in the state of intuition is one of the ultimate aims of humanity.
Advaita vedanta (a school of thought) takes intuition to be an experience through which one can come in contact with an experience Brahman.
Buddhism.
Buddhism finds intuition to be a faculty in the mind of immediate knowledge and puts the term intuition beyond the mental process of conscious thinking, as the conscious thought cannot necessarily access subconscious information, or render such information into a communicable form. In Zen Buddhism various techniques have been developed to help develop one's intuitive capability, such as koans – the resolving of which leads to states of minor enlightenment (satori). In parts of Zen Buddhism intuition is deemed a mental state between the Universal mind and one's individual, discriminating mind.
Western philosophy.
In the West, intuition does not appear as a separate field of study, but the topic features prominently in the works of many philosophers. 
Ancient philosophy.
Early mentions and definitions of intuition can be traced back to Plato. In his book "Republic" he tries to define intuition as a fundamental capacity of human reason to comprehend the true nature of reality. In his works "Meno" and "Phaedo", he describes intuition as a pre-existing knowledge residing in the "soul of eternity", and a phenomenon by which one becomes conscious of pre-existing knowledge. He provides an example of mathematical truths, and posits that they are not arrived at by reason. He argues that these truths are accessed using a knowledge already present in a dormant form and accessible to our intuitive capacity. This concept by Plato is also sometimes referred to as anamnesis. The study was later continued by his intellectual successors, the Neoplatonists.
Islam.
In Islam there are various scholars with varied interpretations of intuition (often termed as hadas (Arabic: حدس), hitting correctly on a mark), sometimes relating the ability of having intuitive knowledge to prophethood. 
Siháb al Din-al Suhrawadi, in his book "Philosophy Of Illumination" (ishraq), from following influences of Plato he finds that intuition is knowledge acquired through illumination, is mystical in nature, and also suggests mystical contemplation (mushahada) to bring about correct judgment. Also influenced by Platonic ideas, Ibn Sīnā (Avicenna) finds the ability of having intuition as a "prophetic capacity" and describes it as knowledge obtained without intentionally acquiring it. He finds that regular knowledge is based on imitation while intuitive knowledge is based on intellectual certitude.
Early modern philosophy.
In his book "Meditations on First Philosophy", Descartes refers to an “intuition” as a pre-existing knowledge gained through rational reasoning or discovering truth through contemplation. This definition is commonly referred to as rational intuition. Later philosophers, such as Hume, have more ambiguous interpretations of intuition. Hume claims intuition is a recognition of relationships (relation of time, place, and causation) while he states that "the resemblance" (recognition of relations) "will strike the eye" (which would not require further examination) but goes on to state, "or rather in mind"—attributing intuition to power of mind, contradicting the theory of empiricism.
Immanuel Kant.
Immanuel Kant’s notion of “intuition” differs considerably from the Cartesian notion, and consists of the basic sensory information provided by the cognitive faculty of sensibility (equivalent to what might loosely be called perception). Kant held that our mind casts all of our external intuitions in the form of space, and all of our internal intuitions (memory, thought) in the form of time. 
Contemporary philosophy.
Intuitions are customarily appealed to independently of any particular theory of how intuitions provide evidence for claims, and there are divergent accounts of what sort of mental state intuitions are, ranging from mere spontaneous judgment to a special presentation of a necessary truth. In recent years a number of philosophers, such as George Bealer, have tried to defend appeals to intuition against Quinean doubts about conceptual analysis. A different challenge to appeals to intuition has recently come from experimental philosophers, who argue that appeals to intuition must be informed by the methods of social science.
The metaphilosophical assumption that philosophy ought to depend on intuitions has recently been challenged by experimental philosophers (e.g., Stephen Stich). One of the main problems adduced by experimental philosophers is that intuitions differ, for instance, from one culture to another, and so it seems problematic to cite them as evidence for a philosophical claim. Timothy Williamson has responded to such objections against philosophical methodology by arguing that intuition plays no special role in philosophy practice, and that skepticism about intuition cannot be meaningfully separated from a general skepticism about judgment. On this view, there are no qualitative differences between the methods of philosophy and common sense, the sciences or mathematics. Others like Ernest Sosa seek to support intuition by arguing that the objections against intuition merely highlight a verbal disagreement.
Philosophy of mathematics and logic.
Intuitionism is a position advanced by Luitzen Egbertus Jan Brouwer in philosophy of mathematics derived from Kant's claim that all mathematical knowledge is knowledge of the pure forms of the intuition—that is, intuition that is not empirical. 
Intuitionistic logic was devised by Arend Heyting to accommodate this position (and has been adopted by other forms of constructivism in general). It is characterized by rejecting the law of excluded middle: as a consequence it does not in general accept rules such as double negation elimination and the use of reductio ad absurdum to prove the existence of something.
Psychology.
Freud.
According to Sigmund Freud, knowledge could only be attained through the intellectual manipulation of carefully made observations and rejected any other means of acquiring knowledge such as intuition, and his findings could have been an analytic turn of his mind towards the subject.
Jung.
In Carl Jung's theory of the ego, described in 1916 in "Psychological Types", intuition is an "irrational function", opposed most directly by sensation, and opposed less strongly by the "rational functions" of thinking and feeling. Jung defined intuition as "perception via the unconscious": using sense-perception only as a starting point, to bring forth ideas, images, possibilities, ways out of a blocked situation, by a process that is mostly unconscious.
Jung said that a person in whom intuition is dominant, an "intuitive type", acts not on the basis of rational judgment but on sheer intensity of perception. An extraverted intuitive type, "the natural champion of all minorities with a future", orients to new and promising but unproven possibilities, often leaving to chase after a new possibility before old ventures have borne fruit, oblivious to his or her own welfare in the constant pursuit of change. An introverted intuitive type orients by images from the unconscious, ever exploring the psychic world of the archetypes, seeking to perceive the meaning of events, but often having no interest in playing a role in those events and not seeing any connection between the contents of the psychic world and him- or herself. Jung thought that extraverted intuitive types were likely entrepreneurs, speculators, cultural revolutionaries, often undone by a desire to escape every situation before it becomes settled and constraining—even repeatedly leaving lovers for the sake of new romantic possibilities. His introverted intuitive types were likely mystics, prophets, or cranks, struggling with a tension between protecting their visions from influence by others and making their ideas comprehensible and reasonably persuasive to others—a necessity for those visions to bear real fruit.
Modern psychology.
In more-recent psychology, intuition can encompass the ability to know valid solutions to problems and decision making. For example, the recognition primed decision (RPD) model explains how people can make relatively fast decisions without having to compare options. Gary Klein found that under time pressure, high stakes, and changing parameters, experts used their base of experience to identify similar situations and intuitively choose feasible solutions. Thus, the RPD model is a blend of intuition and analysis. The intuition is the pattern-matching process that quickly suggests feasible courses of action. The analysis is the mental simulation, a conscious and deliberate review of the courses of action.
Instinct is often misinterpreted as intuition and its reliability considered to be dependent on past knowledge and occurrences in a specific area. For example, someone who has had more experiences with children will tend to have a better instinct about what they should do in certain situations with them. This is not to say that one with a great amount of experience is always going to have an accurate intuition.
Intuitive abilities were quantitatively tested at Yale University in the 1970s. While studying nonverbal communication, researchers noted that some subjects were able to read nonverbal facial cues before reinforcement occurred. In employing a similar design, they noted that highly intuitive subjects made decisions quickly but could not identify their rationale. Their level of accuracy, however, did not differ from that of non-intuitive subjects.
According to the works of Daniel Kahneman, intuition is the ability to automatically generate solutions without long logical arguments or evidence.
Colloquial usage.
Intuition, as a gut feeling based on experience, has been found to be useful for business leaders for making judgement about people, culture and strategy. Law enforcement officers often claim to observe suspects and immediately "know" that they possess a weapon or illicit narcotic substances, which could also be action of instincts. Often unable to articulate why they reacted or what prompted them at the time of the event, they sometimes retrospectively can plot their actions based upon what had been clear and present danger signals. Such examples liken intuition to "gut feelings" and when viable illustrate preconscious activity.
Honours.
Intuition Peak in Antarctica is so named "in appreciation of the role of scientific intuition for the advancement of human knowledge."