Answer
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The process table is a data structure maintained by the operating system to facilitate context switching and scheduling, and other activities. A process table or process control block (PCB) contains information about the process, i.e. registers, quantum, priority, etc. The process table is an array of PCB's, that means logically contains a PCB for all of the current processes in the system.
The process table is needed because in a timesharing system so that the multitude of processes that need to be run can be stored somewhere when they need to be taken off the processor. Then, when it's time to run the process again, it's exact state is known, so it can start back from where it left off.