In a 'box & pan' brake, usually hand-powered, you pinch what will be one leg of the bent part, and sweep the bend to the other leg, in a way that's kinematically similar to making a tubing bend.
In a press brake, you position what will be the center of the bend above the root of a v-die, and force a punch down into it, effectively bending from the center out in both ways at once. You often stop before the punch bottoms out in the die, making an 'air bend', which allows you a variety of nominal radii with one set of tooling. The bent shape actually resembles a hyperbola more than an arc.
There's another kind of hand bend, where you clamp what will be one leg of the part between some rigid metal bars, and beat the remainder of the workpiece down agains one of the bars with a hammer, sometimes with a handheld third bar to distribute the hammer's abuse. It's more labor intensive than using either kind of brake.
Mike Halloran
Pembroke Pines, FL, USA