People who are fickle change their minds so much you can't rely on them. If your best friend suddenly decides that she doesn't like you one week, and then the next week she wants to hang out again, she's being fickle.
Fickle comes from the Old English word ficol, for deceitful. We usually use fickle to talk about people, but it can also be used for abstract things that alternately favor you and abuse you, like the weather. If you win the lottery and then lose everything else in the world that's important to you, fate is being fickle.