It's very hard to define, although just about everyone knows one when he sees one. It usually refers to a guy (I've never heard it refer to a woman), that keeps on falling in love because he has nothing better to do. He loses himself in fantasies of true love and obligations of other people, losing touch with reality. If you try to address him and point out that he should take a more pragmatic approach, he won't know what you are talking about.

An example of a hopeless romantic would be a character like Jay Gatsby from F. Scott Fitzgerald's 'The Great Gatsby'. He is a hopeless romantic because he met 'the one' and for what ever reason, he lost her. All the while he spends his time and resources to find her and it turns out she is married. So because he is so helplessly in love with her, he attempts to get her to divorce. In the end she doesn't divorce and then the only literary thing to do is to kill him off. Basically a helpless romantic is someone who holds a certain unattainable standard for love that he/she will never be able to be happy with out resulting in misery.

Someone who is too romantic, in love with love itself ;) People who are idealists , sentimental dreamers living in fairy tales could also be 'hopless romantic'. When someone is writing love poems ,sending flowers to his lover every day, that is hopeless romantic for example . It could be a positive trait , but if in an exaggerating manner ,it could be used to make fun of someone