Eavesdrop means to listen to a conversation without the speakers' knowledge deliberately.
"He stood behind the door and eavesdropped on their conversation because he wanted to know what they were saying about him".
Overhear means to hear something accidentally; without really meaning to.
"When I was on the bus this morning, I overheard two women talking about the accident. I don't remember a lot of what they said; I wasn't really listening".