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".

overhear is often by accident (although not always). Maybe you overheard two old ladies talking on a bus. You didn't make a special effort to listen to them but you heard their conversation. eavesdrop suggests that you made the effort to try to hear (often secretly). If you stand by a door and really try to listen to the conversation on the other side of the door then this is eavesdropping

The difference is that while one is intentional (to eavesdrop) the other may be not be (to overhear). With eavesdropping a person deliberately tries to hear what is being said in a conversation that he or she is not a part of. When you overhear something, it's usually not intentional.

have you ever tried listening attentively to someone then suddenly, something comes into your mind and regretfully didn't hear the next lines? that was 'overheard'. how about listening to a friend's the same stories again and again where you deliberately focus your attention on something else and just let the voice pass through your ears? that was 'eavesdropped'. :)