Basically, the function of a watchdog timer is to make sure that some processing malfunction does not shut down the entire system. Examples of malfunctions can be hardware failures or a program error that may, for instance, send the program into an infinite loop.
In PLCs, watchdog timers are typically involved with the program scan part of the system. That is, they monitor how long it takes for the processor to scan through the program. If it exceeds some pre-set limit, the timer sends a signal to the PLC processor to stop the program until the problem is corrected.
Getting back to normal operation requires fixing the underlying problem and restarting the PLC.