Here are some control engineering resources that I have written to help people understand some of the absolute basics of control engineering and process control. If you want a really thorough explanation of exactly what a PID controller does and why, then you can't go wrong with my Idiot's Guide to the PID Algorithm. It is the most down to earth explanation of PID Control that you will find anywhere. I absolutely guarantee it!
What the hell is a PID Controller anyway?
The language of Control: describing a PID Loop
Is there an industry standard for PID Controllers?
Understanding the many different flavors of PID Algorithm
The joys of PID Simulation
PID Control and Tuning Articles by Finn Peacock
And here are some external links that show how not to explain PID...
PID Tuning on Wikipedia - a bit heavy on the maths!
PID Control explained by Caltech - I get lost at the swirly diagram thingy