Terminology & description: what are the steps after A Levels I'm a science student currently doing my A levels under EDEXCEL from Bangladesh. I've never really paid attention to or had any counseling about career paths and the steps necessary to finish my studies. I'm even completely clueless about the questions to ask here.

What i particularly want to know about the name and elaborate description about an engineering and Business administration career path. I have loosely heard about terms under graduate, post graduate, masters, Honors, BSc, MBA etc and I have no idea what they are. 

If someone would give me an explanation about the whole system I'd be forever grateful. Thanks in advance to anyone for even directing me to a guideline to learn this things.
A word of warning before I start: while this answer gives the broad strokes, these names and definitions can fluctuate from country to country and field to field. Since we are on Academia SE, this answer is also biased towards reaching a career in academia. If you think you are more likely to want a job in industry, then higher degrees such as Masters or PhDs are often unnecessary.

A Levels

The highest qualification that can be gained during compulsory education in Britain. Students generally take 3 or 4 specialised subjects for 2 years, to prepare them for a job, apprenticeship or university. As you know, this qualification is also found elsewhere e.g. Bangladesh (similar to how IGCSEs are now used around the world).

Undergraduate

A term which refers to both a first degree and the person who is taking it, for example, "I did my undergraduate at University X" or "I am an undergraduate in physics". Often shortened to "undergrad" (in the UK).

Post-graduate

A term which refers to someone who has obtained their undergraduate degree i.e. they are post-graduation, and is now studying for a post-graduate degree, for example a Masters or PhD. Someone who has obtained their undergraduate degree but is not pursuing further study would be referred to as a graduate.

BSc/ BA

These are types of undergraduate degree (Bachelor of Science, Bachelor of Arts). These are normally obtained after three or more years of study in a university (aka college in the USA). The type of degree depends on your field of study, for instance, a History degree might be a BA, whereas a Biology degree would be a BSc.

MSc/ MSci/ MA/ MFA/ MBA

These are all types of Masters degrees, typically lasting one year or more and taken after an undergraduate degree. Sometimes these are completely coursework based and simply teach the student more specialised knowledge about a particular subfield; sometimes they are research based and designed to prepare the student for a career in research.

PhD

The highest academic qualification. People with this degree can use the title of "Doctor". Can last anywhere between 3 years (Europe) to 5+ years (USA). Generally there is little to no coursework and the degree is obtained by performing original research and by defending a thesis.

Honours degrees

This is a very loose term that can mean different things in different universities and countries. At my university, to graduate with Honours means that you didn't fail any courses during your degree.

Advice

I would highly recommend speaking to your teachers or any kind of career advisor at your school about what you should do once you have finished your A Levels. For a career in engineering, I think a BSc would be the minimum requirement (business administration I'm not so sure about).