When a process is swapped out of the processor by the scheduler it will need to store the current state of the process. This includes -

This information is packaged together and stored onto a stack. When the process is to be run again it will need to restore the all of the data stored so the process can pick up where it left off. The program counter will say what instruction it got to while the other stored data will supply the state of the process.

If this information was not stored then a process could not resume or could crash the system.