An anecdote is a story that is told in order to convey information or to provide an example. Sometimes humorous, anecdotes not only provide information but also have a purpose.
For instance, imagine a conversation starts up regarding car troubles - your coworker then tells a ridiculous story about a flat tire and how always having a spare tire is important. The coworker just told an anecdote.
In legal settings, anecdotal evidence refers to personal testimony and other subjective evidence that isn't backed up scientifically. An example of anecdotal evidence would be a witness who casually talks about the strange behaviors of the defendant. Although this might be relevant to the case it's not officially documented in any manner (such as with photographs, videos, scientific observation, etc) - therefore it's anecdotal.