Stephen Colbert had big balls when he skewered the White House Corespondents and lampooned the Bush Administration at the White House Correspondents Dinner 2006.
In the game of pool, the big balls are the stripes, as opposed to the solids, which are called small balls. One can imagine that the solid-colored balls look smaller than the stripes, although they are all identical except in appearance.
Usually used in the gym when you're trying to convince someone to do more reps. Can also be used in other situations when you are trying to make someone do something.