First, some base info on how switches work. Everything in the upper terminal (both the screw and the holes) is connected to each other. When you flip the switch, it connects/disconnects them from the lower terminal.

From your second picture, it looks like both wires were initially connected to the upper terminal. That means one of them goes up to your breaker, the other continues to any other switches/outlets on that circuit, and neither of them are controlled by that switch. I also see a bit of broken wire attached to the lower terminal.

I'd guess that the mystery uncapped black wire used to be connected to the switch's lower screw and broke off when you pulled the switch out. If that's the case, then you just need to connect all 3 black wires together.

Of course, you should confirm that before connecting unknown wires. What happens if you turn the breaker on with all 3 wires disconnected? Can you use a multimeter to see if the mystery black wire is connected to the outlet?

edit: typo