As your pads wear, they get thinner, so the pistons have to extend outward to keep the pads pressed to the disk. You'll notice the fluid in the reservoir getting lower as that happens.
When you install new pads, you need to force the pistons back into the caliper, back to their "new-pad" position. This involves pushing fluid back through the hydraulic line into the reservoir, and requires some force to do. You can usually do it just with your hands, but a clamp makes the process more controlled and gradual.
That's also why you should remove the cap to the reservoir before installing new pads. That keeps an "air spring" from forming in the top of the reservoir and making the piston retraction process more difficult.
Edit: Also, DO NOT put ANY pressure on the rotor as you work on the brakes! You'll knock them out of true, and even a couple of mils will make your brakes pulse or worse. Keep those babies as straight and true as you possibly can; they're plenty good at going out of true all by themselves.