Ken, this is a HUGE subject. In the old days you would use relays in a switchboard to control things in factories and buildings. You'd also use timers, thermostats, limit switches, position sensors etc to control the relays which would then switch things (motors, machinery, etc) on and off.Then someone invented PLCs. A PLC does the same as the relays did, but using digital logic and (these days) microcontrollers. PLCs can use Ladder Logic, which is a system of representing inputs and outputs in the same way we used to use sensors and relays.The advantage of a PLC is that if you want to change the operation of a complicated machine, you don't need to rewire a switchboard, which is time-consuming and costly. You just change the program of the PLC, which is quicker and easier.I could write a whole series of columns on PLCs so it is better to direct you to a good website that has more detail than I can put here. The best one I have found is http://www.plcs.net/contents.shtml
I am sure you will find there answers to all the questions you have, this is a really good site.If you are interested in going further, many technical colleges do courses on PLCs, or you can buy one yourself and program it with your PC, small PLCs cost only a couple of hundred dollars. Make sure you get one with Ladder programming - most these days connect to a PC and have a downloadable programming software, but some have an LCD display and small keyboard so they are self-contained.Good luck with this, it is a very interesting subject.