What is a Logic Programmable Controller (LPC)?

They are typically used to control some sort of process, say heating, cooling or adding chemicals into a production line or waste water system. They can controll just about anything valves, fans, motors, pumps.
They have inputs which may be simple switches, variable currents or voltages, and the drive outputs which can be simple contacts or whatever you need.
Basically they are a micro-controller in a box with some inputs and outputs made available to the user, and some sort of user interface to allow programming.

They can be used for many purposes, so that you don't need to design a new controller for every process you wish to control.

Del

Typically called PLC's in the US (as in Programmable Logic Controllers). They are basically computers built for easy interfacing with process components with inputs and outputs either conditioned or not. These days, most PLC's don't need external signal conditioners.