A digital computer used for automation of typically industrial electro-mechanical processes.
What is a plc?
Here is a short video to add upon Hippy's answer. Hope it helps you out !
I work with PLC's all the time, I've been in the electrical industry for about 40 years. Back when I first started PLC's didn't exist, we used relays and timers to accomplish any processes that were needed in a machine, the cabinets were huge, and required a lot of extra wiring between each of the relays ect. Today the cabinets have shrunk using only a few relays for safety devices and interlocks between cabinets inside of a system. All of the relays/timers are now virtual along with many more "devices" being able to create, within the program. These additional devices such as Latches, Bit shifts, Fifo's, and such, make modern process possible that could not have been done with older relay logic. The video that Rooster posted is pretty good, however, not all modern equipment is PLC ran, there are process programs that are PC based, rather than PLC, but the most common is PLC.