If you want to pause a process while you do something else, like for instance stop a heavy file operation while you're just moving some stuff around quickly, there are two signals to pay attention to: STOP and CONT.
STOP will pause a process (not actually stop it - it doesn't die)
CONT continues a stopped process, and does nothing if the process isn't stopped.
An easy way to experiment with this is to start xeyes:
$ xeyes &  26114
In this case, xeyes got the Process ID (PID) 26114. You can use "ps" to find Process ID's of running processes.
To pause this process I use, in my case "kill -STOP 26114". Notice the eyes stop moving to follow the mouse pointer. "kill -CONT 26114" resumes the application.