River was born with the power to regenerate but used up all her remaining regenerations when she saved the Doctor after she poisoned him because she was programmed to kill him... Very complicated.
He first met her on the planet of The Library, so her journal is (or will be!) packed with information the Doctor feels he shouldn't know about yet. The tragedy is, he knows how River dies, so when the two of them have that picnic at Asgard and do whatever they did together at the Singing Towers, he'll have a terrible secret that he won't be able to tell her.
River shares the Time Lord's buccaneering sense of adventure, as well as his knack for getting into trouble. But as for just how much they meant to each other: spoilers!