An anecdote is simply a true story that is generally amusing, thought-provoking, etc. and most commonly refers to some subject the speaker is talking about.
If someone were talking about the misuse of law enforcement, for example, they might tell a story about how a man in charge of road cleanup was ticketed for littering when a scrap of paper he had already picked up off the road blew out the back of his truck.
An anecdote is a brief story about something amusing or strange.