They are nonprofit organizations where Mac users come together and talk about, well, all things Mac.
MUGs are usually geographically based, and have anywhere between a handful and thousands of members.
Those with knowledge share that knowledge with those who seek it. The common bond is almost always a love for the Mac. Consider the history of such groups. MUGs have their roots in earlier Apple User Groups and other hobbyist organizations which sprang up when Apple introduced the Mac in 1984. They hit their peak in the mid-1990s when Apple was flying high on the house of cards that John Sculley built.