+1 It seems like there are a variety of sounds made by the actuators on various Prii. I can't think of anything else that would make continuous noise if you press on the brake unless there was some huge malfunction and it was squirting brake fluid on the pavement.
What I hear starting at 0:18 is the usual stretchy noises from pressing the brakes hard, plus a little high-pitched squeak on applying the brakes or on releasing them. Just sounds to me like a place where some metal moving on metal could use a new dab of grease. It's a Gen 2, so I'd probably start looking at the rears (unless you're sure it sounds like the front, in person), just because the drum brake mechanism has more stuff to slide around. -Chap