Caleb - I think you are confusing several things. PWM and PID are unrelated concepts.
Feedback is the idea that the reading from a sensor monitoring the process is an input into the control of that process. Let's say you're driving your car (along a straight, unoccupied road). If all you care about is getting to some point further down the road, and the speed doesn't matter, then you turn on the engine and push down the pedal until you arrive. That's open-loop control of the speed - no feedback. If instead you want to drive exactly 50 km/h, then you start looking at your speedometer and adjusting the pressure on the pedal - that's feedback.
PID is one algorithm for closed-loop control, where closed-loop means that there is feedback in the system.
PWM is a way turn a binary (on or off) signal into a continuously-varying signal by turning it on or off rapidly. Often the output of a PID loop drives a PWM signal, but PID can drive any type of analog output. Going back to the car example: modern cars use fuel injectors to control how much fuel enters the engine. An injector is a small valve that's either open or closed. The accelerator varies the amount of time that the value is open versus closed (the "duty cycle") depending on how hard you push on the pedal. That's PWM. Although the valve can only be open or closed, it can control the flow rate over a wide range by cycling rapidly between the on and off states.
