macOS keeps a short list of things an app may only do with your say-so, and puts the switches under System Settings → Privacy & Security. Accessibility is the one that covers "watch the keyboard and control other apps' windows". It was designed for assistive software, and it is the same mechanism every keyboard remapper, window manager, clipboard manager, text expander and automation tool uses, because no other mechanism exists for those jobs.
What it allows: seeing key presses and mouse clicks as they happen, sending its own, and reading and moving other apps' windows and controls. What it does not include: reading files, the camera, the microphone, your screen (that is Screen Recording, a separate switch) or your location.
So the question is always the same: do you trust this app enough for that? Things that help you decide:
- The app is notarized (macOS checked it opened without the "could not verify" warning).
- It explains what it uses the permission for, before asking.
- It states, in writing, what it does with what it sees.
To grant it: the app usually opens the right pane; turn on its switch. To revoke it: the same pane, switch off or press the minus button. macOS ties the permission to the app's signature and may drop it after an update; adding the app again fixes that.