It's a lever attached to the bottom of the rifle.
It allows:
1. The stock to remain in-line with the bore of the rifle.
2. Additional leverage to control recoil.
3. Quicker and more intuitive return of the weapon to-shoulder after running or changing magazines.
4. The wrist to remain in a neutral position when depressing the magazine release button.
The Sten, BAR, and the PPSH were pretty much the last generations of fully-automatic rifles to use a horizontal grip configuration, and in both cases, (Soviet and Western) weapons designers converged on the pistol-grip for subsequent designs of the autoloading light rifle, despite substantial differences in design between the M16 and the AK-47.
Why did they make the change? All three of those weapons (Sten, BAR, PPSH) were in widespread combat usage at the time, as were horizontal-grip semiautomatic rifles like the SKS, M14, and M1 Garand/Carbine (as well as a variety of horizontal-grip bolt-action rifles). Why not keep the same configuration for the next generation of rifles so that soldiers would be using the same basic setup that they had originally been trained on? Why did the StG 44, AK-47, Thompson, and later the M-16 all make the switch? Even the Swedes started adding pistol-grips to the BAR in the twenties.
Horizontal-grip rifles just don't seem to be as well-suited for controllability of fully-automatic, or rapid semi-automatic fire.