River Song is an archaeologist from the future who the Doctor keeps meeting in the wrong order.
He first met her on the planet of The Library, but we haven't yet seen where she first met him. Her journal is packed with information the Doctor feels he shouldn't know about yet. They are going to be very close: River knows the Doctor's real name, she has a sonic screwdriver of her own and she even knows how to fly the TARDIS. The tragedy is, the Doctor knows how River dies, so when the two of them meet at the crash of the Byzantium, share that picnic at Asgard and whatever they did together at the Singing Towers, he'll have a terrible secret that he won't be able to tell her.
River has a knack for getting into trouble and knows the Doctor can help her get out of it. But as for just how much they mean to each other: spoilers!