That's the thing, we don't know... yet? All we have at the moment are implications about their relationship. It's assumed, because of the fact she knows his real name (a fact not even avid watchers of the show know) assumes they were unusually intimate (even more than with Rose and, possibly, Martha); this seems to be reinforced by the fact that the Doctor gives her an improved Sonic Screwdriver, containing a Neural Relay (her "digital essence" in a way), plus (possibly) their picnic at Asgard.