Master's Degree

An academic qualification one level up from a bachelor's degree. It normally involves more self-guided research than a bachelor's and is considered by some to be preparation for a PhD or DPhil.
If you get a bachelor's degree from Cambridge or Oxford in England then a few years after graduation you automatically receive an MA.
Bizarre!

The Master's is the degree one level up from the Bachelor's degree in English-speaking academia. (In Germany, for instance, the first degree you receive is the Magister degree; this is somewhat similar to a taught master's, but not really). Typically you will acquire this if you can't be bothered to get a doctorate (or if you suck). These degrees come in several, fairly different flavours:

Taught Master's

This comes in two major varieties: the post-graduate MSc/MA, and the under-graduate Mα, for α in {Eng, Math, Phys, Chem...}. The first kind is acquired by getting a bachelor's, then doing one year of a taught course, assessed by exams.

The second kind is new to the UK. This involves doing some years shared with the related bachelor's course, then branching off, typically in the third year. The course runs for four years. The major advantage of doing it this way is that as this is available as a first degree, it is cheaper than the first approach. Also, many MEng degrees (Master of Engineering) fulfil all the educational requirements for the appropriate engineering charter.

Research Master's

1 year, one dissertation, get MSc/Ma.

MPhil

Master of Philosophy. This is the superconsolation prize awarded to those narrowly failing to get a PhD.

Just to confuse everyone, Cambridge awards the MPhil as it's standard taught master's qualification.