It's actually called a surcingle. It's for extra security and to make stock saddles legal in competitions where you must have two points of security - Such as polocrosse and PC in Australia.
This is my saddle when I first got it (hence the leather looks very stiff). This shot shows how the surcingle sits over the seat of the saddle and then threads through slits in the skirts so that is can attach to the girth. It has one end with holes that you use as the second girth point on one side, and the other side has a ring - This is where the strap on the girth comes in. You thread it up through the ring and back down to buckle, so you have some leverage to get it tight enough.
Here is a shot from further away - This is the side with the ring, hence only one girth point can be seen.
And the other side - You can see that the surcingle has come down and buckled into the girth just like a normal girth point.
What you can't see in these pictures because the saddle has never been ridden in and isn't broken in - There is an indent in the seat made for the surcingle to sit in, so it isn't uncomfortable while riding. It also sits over the top of the small flap protecting the stirrup leathers.