There’s what seems to be a pretty good explanation of Bitcoin, and how it works, here (h/t Bruce Schneier). It goes into detail on the use of crypto (mostly digital signatures), and on other techniques intended to avoid cheating.
For myself, I am not currently using Bitcoin. I’ll wait to see how use of it settles down before I decide whether to join in.
What is interesting, is the way that it uses crypto, and the way that it manages distributed control so that there is no central bank. This latter aspect is what has some governments concerned, for they do not like the idea of a banking system that they cannot regulate.