Well I'm no expert, but MSc is Master of Science, MA is Master of Arts, MEd is Master of Education, MBA is Master of Business Administration, and MPhil is Master of Philosophy - it's a lesser degree than a PhD, and is sometimes awarded to PhD students who marginally fail. See http://en.wikipedia.org/wiki/Master_of_Philosophy for more info on that one.
Squiggles is right. Basically, just to simplify, you must choose the one which is relevant to your field. For example, if your subject is an arts subject, you would do an MA. If you are in the sciences, you would do an Msc and so on.
MScs and MAs are usually taught degrees where you have regular lectures and are expected to learn a body of knowledge in addition to doing a small research project. MEds are qualifications for education and can be vocational or around developing pedagological skills.
MPhils and MRes are research degrees that don't normally have taught components. They normally are about half the size of PhDs but have a larger research component than an MSc/MA. The difference between the two is slight, but MPhils are now usually awarded to PhD students that decide not to upgrade, whereas MRes students usually sign on to do a finite piece of research for a shorter amount of time and start out with the intention of doing a Masters level research degree.
i'm going to be doing a 1+3 programme where the first bit is a taught MRes (with some research and a small thesis) and the second bit is the PhD (with more research and a big thesis).
LLM – Master of Laws MA – Master of Arts MArch – Master of Architecture MBA – Master of Business Administration MEd – Master of Education MEng - Master of Engineering MFA – Master of Fine Art MLitt – Master of Letters MMus – Master of Music MPharm – Master of Pharmacy MPhil – Master of Philosophy MRes – Master of Research MSc – Master of Science MSt – Master of Studies MTh – Master of Theology