If a person has an idiosyncrasy, he or she has a little quirk, or a funny behavior, that makes him or her different. If you only say goodbye in French, never in English, that would be an idiosyncrasy.
Idio seems like it means stupid, but really it is Latin for "one's own," as an idiosyncrasy is one's own particular, usually odd, behavior. Putting salt in your hot chocolate or needing the light on to sleep or tapping your head while you think are all idiosyncrasies. A machine such as a DVD player has an idiosyncrasy if you have to do something weird to it to make it work like having to bang it on the back left-hand side to stop it from skipping.