Count noun

In linguistics, a count noun (also countable noun) is a noun that can be modified by a numeral and that occurs in both singular and plural forms, and that co-occurs with quantificational determiners like "every", "each", "several", etc. A mass noun has none of these properties, because it cannot be modified by a numeral, cannot occur in plural, and cannot co-occur with quantificational determiners.
Examples.
Below are examples of all the properties of count nouns holding for the count noun "chair", but not for the mass noun "furniture". 
Some determiners can be used with both mass and count nouns, including "some", "a lot (of)", "no". Others cannot: "few" and "many" are used with count items, "little" and "much" with mass. (On the other hand, "fewer" is reserved for count and "less" for mass (see Fewer vs. less), but "more" is the proper comparative for both "many" and "much".)
Grammatical distinction.
The concept of a "mass noun" is a grammatical concept and is not based on the innate nature of the object to which that noun refers. For example, "seven chairs" and "some furniture" could refer to exactly the same objects, with "seven chairs" referring to them as a collection of individual objects but with "some furniture" referring to them as a single undifferentiated unit. However, some abstract phenomena like "fun" and "hope" have properties which make it difficult to refer to them with a count noun. 
Classifiers are sometimes used as count nouns preceding mass nouns, in order to redirect the speaker's focus away from the mass nature. For example, "There's some "furniture" in the room" can be restated, with a change of focus, to "There are some "pieces" of "furniture" in the room"; and "let's have some "fun"" can be refocused as "Let's have a "bit" of "fun"". 
In English, some nouns are used most frequently as mass nouns, with or without a classifier (as in "Waiter, I'll have some "coffee"" or "Waiter, I'll have a "cup" of "coffee""), but also, less frequently, as count nouns (as in "Waiter, we'll have three "coffees".")
Theory.
Following the work of logicians like Godehard Link and linguists like Manfred Krifka, we know that the mass/count distinction can be given a precise mathematical definition in terms of notions like cumulativity and quantization. Discussed by Barry Schein in 1993, a new logical framework, called plural logic, has also been used for characterizing the semantics of count nouns and mass nouns.
Linguistic differences.
Some languages, such as Mandarin Chinese, treat all nouns as mass nouns, and need to make use of a noun classifier (see "Chinese classifier") to add numerals and other quantifiers. The following examples are of nouns which, while seemingly innately countable, are still treated as mass nouns:
A classifier, therefore, implies that the object(s) referred to are countable in the sense that the speaker intends them to be enumerated, rather than considered as a unit (regardless of quantity). Notice that the classifier changes as the unit being counted changes.
Words such as "milk" or "rice" are not so obviously countable entities, but they can be counted with an appropriate unit of measure in both English and Mandarin (e.g., ""glasses" of milk" or ""spoonfuls" of rice").
The use of a classifier is similar to, but not identical with, the use of units of measurement to count "groups" of objects in English. For example, in "three shelves of books", "shelves" is used as a unit of measurement.
On the other hand, some languages like Turkish treats all the nouns, even the not so obviously countable entities as count nouns.
Even then, it's possible to use units of measures with numbers in Turkish, even with the very obviously countable nouns. Note that the Turkish nouns can't take a plural suffix after the numbers and the units of measure.