A Programmable Logic Controller (PLC) is a ruggedized special purpose computer that reads input signals, runs control logic, and then writes output signals. They are used in factory production line automation mostly, but can be used in very many other applications also.A PLC (i.e. Programmable Logic Controller) was invented to replace the necessary sequential relay circuits for machine control. The PLC works by looking at its inputs and depending upon their state, turning on/off its outputs. The user enters a program, usually via software, that gives the desired results. PLCs are used in many "real world" applications, like industrial control. If you are involved in machining, packaging, material handling, automated assembly or countless other industries you are probably already using them. Almost any application that needs some type of electrical control of machine has a need for a PLC.
A PLC works by continually scanning a program. First the PLC takes a look at each input to determine if it is on or off. Next the PLC executes your program one instruction at a time. Finally the PLC updates the status of the outputs. It updates the outputs based on which inputs were on during the first step and the results of executing your program during the second step. In the beginning all PLC implementations were proprietary, but nowadays there is standardization in this field going on.
The standard interfaces used in PLCs are most typically digital input (24V binary input), digital output (solid state or relay),analog input (4..20 mA current loop) and analog output (4..20 mA current loop).
The PLC is basically a ready made device that includes a microcontroller, interface electronics (between real-life industrial typically 24V very robust interfacesas and microcontroller 5V logic signals) and a special control software (designed to work reliably and have pissibly built-in safety features).
More information on PLC can be found at
http://www.epanorama.net/links/automation.html#plc
The diference between PLC and PIC is that the PIC is just the bare microcontroller IC, while the PLC is a whole tested product based on some microcontrontroller.
You can built a PLC like device based on PIC. Then you need to add some electronics aroudn the PIC (input and output circuitry) and then your control software that does the necessary controlling. It is possible, but time consuming to do this all. Designing a device that will reliably work on hard industrial environment is fat from easy. Baddly designed simple PIC (or any other microcontroller) based circuitry can easily "crash" / fail / get damaged if it is exposed to voltage spikes you can see in industrial control enviroments.