There's a lug that comes out the other end which has a spring inside the bolt that the screw pushes down on so that the lug is pushed down even if the lug rubs against the hammer and pushes it upward. The lug cocks back the hammer, when you pull the trigger the hammer hits the valve.
The safety is known to come apart, your best bet is just leave it out. Plus you really don't need a safety on a pump anyways, I could see a semi maybe.
When I traded for my pgp the safety was broken, well not broken, just need a ball bearing and spring. I didn't want to have to deal with it, and since there was no spring or ball bearing holding it in place, it would slide around and engage the safety when I didn't expect it. So what I did is I took a small nail and shoved it in the hole on the top where the spring and bearing go and then cut the remaining nail off.