I am probably being way too simplistic with this, but I think she is another timelord, he was wrong to think they were all dead and she is his wife.
She said shall we check diaries in the plural, which would suggest she also flits about in time and they meet up occasionally when and where they can, so she likes to get a check on where abouts in their real time they are whenever they meet up. She just hadnt met him before outside of their own timeline. Does that make sense?
If its not that, then she is another incarnation of the Doctor himself.