There's another idea in the second post
Like most things, it started quite unexpectedly... They were called into the office by Dumbledore and told that they would all be introduced to something both dangerous and wonderful at the same time. Some sort of other form of magic that was, perhaps, not magic at all - old magic that had been since locked and sealed away but, as Dumbledore often did, he decided that a little rule-breaking was warranted in this time of... great need.
And so it was decided that the portal should be opened and that a member of the other universe - their alternate universe - should be added. It was very conceited to believe that their world was the only that existed in the vast nothingness (or somethingness) of space, or that there were not other creatures like them at all, and so it came both as a shocking surprise and... a form of validation to those who were allowed to actually see what he had to show them.
"There are things from which we can all learn," he said, "From our brothers, our counterparts. Things to be opened that were before unimaginable. I had hoped to keep this hidden for just a while longer, hoped to keep them and us safe. It is clear to me, though," he turned away from the group, hands folded neatly at the end of his beard, "That we are in need of a little help..."
He acted as though it was his first time venturing through that particular portal but, as many who knew Dumbledore would be able to tell, it was far from his first time. In fact, he had already chosen the particular person to be introduced to their world.
"There is a Lily... male, but brave, noble like our own friend... There is the James, the Sirius - both have survived thus far... There is the Hagrid and," he gave a light chuckle, smiling to himself, "Even a Dumbledore! He is quite a handsome fellow, if I do say so myself - rather rugged and young." As he walked about he desk he ignored the frightened, confused stares of the damaged comrades, "But I think, for this particular assignment... it may be best to employ... The Snape."
Many were confused - of all of the people to bring in from that universe, that other place, why Snape? Surely they could make use of another... They could bring in Lily's counterpart, James', someone more noble. Why the least trustworthy? Snape was trusted insofar as Dumbledore said he could be... And so why should 'The Snape' be brought in of all people...
This game will explore the idea of an alternate universe. Dumbledore realized that Snape's mission would be to take care of Hogwarts in his absence and, to make absolutely sure, he wanted to give him help - he called his counterpart from the other universe using a type of unknown, little-used magic from the old ages to do so. Such is dangerous because it is possible that Voldemort would be able to take his own counterpart and use him to destroy both worlds, but Dumbledore is willing to take the risk.
The female will be similar to but not exactly the same as Snape. For example, in her universe she actually did get with The Lily, and various other differences about her past that make her quite different from Snape. Their way of thinking is the same, though: Do what needs to be done in any way that it will take to do it.
Their mission is to help one another hide their intentions from the Dark Lord while simultaneously aiding Harry on his quest.
I will answer any questions anyone has about this, but for now I leave it rather vague (in terms of my own expectations) so that it can grow!