Motherboard Chokes and Caps?

What is the purpose of the "capacitors and "chokes" that we see on motherboards?

What do they do for the different Ports/Chipsets/Peripherals?

I've heard somewhere that, fundamentally, capacitors are little batteries that hold a certain charge of power, in the event that there is some irregularity in the power delivery, the capacitor will drain it's power into whatever it is wired to. I know that sounds primitive but if that is true, please expand on it, and if not, please correct me.

I also want to know the capacitors on a MOBO different from those found on a CPU chip or memory cell, past the size differences of course.

Additionally, I want to know how the difference materials that chokes and capacitors are made out of affect their performance.

Also the difference between Liquid Caps and Solid caps, weaknesses and advantages of each.

Finally, I would like for someone who actually knows what he/she is talking about to answer me. I don't want a overly simplified explanation of each component, go in depth as possible, excluding any terms that would deal with a dimension you are not likely to talk about. And try to source material. Thanks!