Well, I guess I'll be the first to take a stab at it, but keep in mind that this is a very 'individual' answer.
I define it as something that is capable of 'moving' me emotionally to another level that I wasn't previously at before listening. Another definition would be a piece that I can visualize mentally what is happening.
I don't think this fits any particular style or genre or is attributable to any particular person. There have been multitudes of great songs that I've listened to. It's a list too long to type. But I think most people can pinpoint a lot of them by their lasting impression on the field of music and whether or not you as an individual like it or understand it takes second place to the fact that it has contributed in some way to the evolution of the genre its a part of. Any music that touches a lot of people is considered great by those that were touched by it. Those that weren't don't understand. Should that lessen its greatness or impact? I don't think so. I don't understand or appreciate a lot of the classics or rap or country, but the are people that do and for those people they consider some of it 'great' music. Who am I to detract from that? It's obvious by the lasting power of some of the musicians in those genres that their songs are 'great.' They've moved their particular audience, so they've achieved some level of greatness, IMO.
Its a very difficult and sometimes vague question. I don't think its easily answered. So, I'll cut my response short and say that if it touches my heart, engages me, enrages me, scares me, makes me cry, makes me laugh, brings out the human in me, if it touches me emotionally in some way, if I connect with the artist through the music, then to me its a masterpiece with no equal.