Commander X16

I have this function: And before you ask how this works, I don't know either. All I know is that it's supposed to jump to $8001 in memory.

When I make a program that calls this function and run it in the emulator, it gives me this screen: It only triggers sometimes and I can't figure out when. Sometimes the program will just exit normally without showing this screen. What does this screen actually do?

You are entering the monitor program that is stored in ROM.
This usually happens when your program "runs off into the wild"

If you just "call" address $8001 without knowing what is there, strange stuff is most certainly going to happen

You can think of the monitor as the "Oh no, the program crashed" screen, since that's when most people are going to see it.

The purpose of the monitor is to allow programmers to check/modify what's currently in RAM, whether that's program variables, data, or actual code, in order to help debug a program. You can go back to BASIC by typing an X and pressing enter, but it probably won't resume the program.