What's the difference between a folder and a bin?
They both can hold stuff, right? (clips, sequences, photos, etc)
Is it that the bin gives the extra functionality that a folder doesn't?
In FCP, the folders are actually called bins. There's a lot of differences in how they act in FCP & Avid, though. Avid bins exist outside the project file, FCP bins do not. In FCP, you can stack bins inside of other bins, in Avid you cannot. The manuals will give a lot of insight.
The term 'bin' is a holdover from the days of film, where the editing room had cloth-lined metal bins full of film. There are hooks at the top of the bin that are used to hold the beginning of each cut of film. Avid wanted to be film-friendly in the early years and adopted this term.