A consolation prize is when you ask a girl out and she says no but she wants to remain good friends. The guy feels like he is not good enough for a romantic relationship just a platonic friendship.
This usually occurs between friends; the guy and the girl start as friends however the guy starts to like her romantically and wants their friendship to develop into a relationship. When he lets his feelings be known to her, she turns him down but honestly tells him she wants him as a friend. At this point the guy needs to do some soul searching and figure out if they can go back to the way things were or they go their separate ways.
Sometimes girls will say this to a guy they don't know well as a subtle cue to go away. However this most often happens between friends and has the ability to destroy friendships. The guy has had his pride hurt and is left resentful and bitter and feels like he has been made a fool of by the girl who he thought so much of.
The girl is left hurt as well, since she feels guilty about hurting him and possibly losing a close friend. However she can quickly get annoyed at him if she thinks he's being immature or trying to guilt trip her into a relationship by acting depressed. Its an awkward situation and requires much tact and patience for things to turn out alright.
John Doe 1: "I ask Jane Doe out yesterday."
John Doe 2: "How did that go?"
John Doe 1: "I got the consolation prize...she wants to be friends."