what exactly is that little dirt stain that moves from cylinder to cylinder supposed to be? is it supposed to represent tension or something?

It's the currently binding cylinder. With the right amount of tension applied via the wrench, one pin binds at a time, which is what allows you to set the pins one at a time.

What's the difference in feeling where he's 'testing' which one's the binding cylinder or not? Is it just a tiny bit more 'grainy' harder to push or something?

The binding pin won't bounce up and down when you actuate it with the pick. The non-binding pins won't offer any resistance at all. Also, when you manage to get the binding pin to the shear line, the tension wrench will sometimes give up a little more rotation.

why does only one cylinder bind at a time?

It seems to me like the lock shouldn't be able to turn at all until all of the cylinders are pressed to the right height.

Due to imperfections in the lock. It only takes a tiny difference for that tension to not be applied evenly so you can focus on one pin at a time.

Manufacturing tolerances aren't 100% perfect.

it's the next 'key' pin. (the little stain is a key icon.)

Interesting. What is that little gold-ish looking thing that moves from one pin to the other in this gif?

When you turn a lock, small machining defects mean that more load is borne by one pin than the others. Pushing up that pin while applying torque (using the allen wrench in the GIF) will cause that pin to be held up, which applies more load to some other pin.

It's suppose to show you which pin is the correct one. The lock picker obviously can't know that's why he tries all of them.

This is what you're after. http://toool.us/deviant/index.html

The "MIT Lockpicking Guide" covers the subject nicely, if you are just interested in how it works. A slick gif would be nice though.

That's what I was thinking. That would be quite nice.