What is the story behind the 'wall girl' in the movie "Deep Dark"?

This is discussed by the Director in a series of interviews and podcasts

In short, behind the hole is a monster. It's not an (especially) evil monster so much as powerful and callous:

That scene just felt so compelling to me—I eventually created the rest of story around it. But rather than have the Hole be an evil creature, I wanted to portray her as more of a misunderstood, albeit powerful, monster.

As to quite why there's a monster hiding behind his wall, that's never revealed. This is simply the central conceit of the film and is glossed over with an airy hand-wave:

The Hole is really just a voice in a wall. With no arms or legs, if she needs get something done she requires other people to do it. So her voice needs to be compelling enough to manipulate people. While writing the script, it helped me to already have a voice in my head for The Hole. For me, that was the strong yet seductive voice of Aeon flux.