When you pull the trigger the sear drops out of the way of the cocking piece and as you lower the bolt handle the cocking piece simply rides back down the camming angle (the "V" cut) cut into the back of the bolt body.

You are simply lowering the cocking piece and firing pin with out actually dry firing the gun. Same exact concept as pulling the trigger on gun with an exposed hammer (like a Marlin or a revolver) and letting the hammer down with your thumb instead of letting it dry fire only the camming angle on the bolt body is acting as your thumb.

BTW, dry firing your rifle will not harm it in the least. It is perfectly safe to do so as long as it is unloaded.

You also do not have to pull the bolt all the way back to do what your friend showed you. You simply have to have the handle in the up position.