Warping

You've noticed, when applying the brakes, that the brake pedal moves up and down under light pressure and that you (may or may not) feel a slight shimmy in the steering wheel. What is it?

The answer is: you probably have a warped brake rotor or rotors.

Some cars are worse than others where warped rotors are concerned.
Disc brake pads are in constant contact with the rotors. Pads and rotors can run extremely hot, as can be seen if you've ever watched "under the car" shots of brakes on race cars. The rotors will be glowing red and the same can be true with passenger cars and trucks, especially if you're towing, hauling a heavy load, going downhill, on a crooked road or any driving situation where you're using the brakes a lot.

In the past, when cars and trucks only had drum brakes and we ran through water that got the brake shoes wet, it wasn't unusual to have lots of pedal, but no brakes. Disc brakes eliminated most of that problem and the majority of brake fade that was also associated with drum brakes. Now, with disc brakes, if the rotors are hot and we run through water cooling the rotors too quickly, the rotor will warp. If you heat a piece of metal and then quickly place it in water, you can see the effects of quenching. The metal will twist, move and warp until it cools to the approximate temperature of the water. This is the process used when tempering metals. It makes the outer surface hard, and if done correctly, it leaves the inner parent metal pliable. But, the item has to be machined flat if precision is necessary, as is the case with disc brake rotors.

Running through water isn't the only reason rotors warp.
If the piston in the disc brake caliper isn't releasing properly, the brake pad will put too much pressure on the rotor and the ensuing friction won't allow the rotor to cool. There are different types of calipers and caliper mounts, and some are more prone to sticking than others. Some cars have calipers that slide back and forth on the part that's bolted to the wheel spindle assembly. If enough dirt or road grime gets between the sliding parts, the caliper can stick and not allow the pad sufficient clearance for cooling.