A square is a tool used for accurately measuring angles, especially right angles. A granite square is one made out of granite.
Most squares look something like an L (the L square and try square look exactly like an L), but granite squares are just a slab of rock so they are usually either a triangle or a square, or, in some cases, a cube. Being made of stone they are resistant to warping through use or humidity, won't flex significantly due to temperature, and can be buffed to a very high precision edge -- it's not uncommon to see one advertised as accurate to .00005 of an inch. As you might expect, these are not used for anything much other than precision machining, most often to calibrate CNC machines.
You will not find the professional grade granite squares at your local hardware store; they often weigh 200+ pounds, and often cost somewhere between $1000-4500. You can buy cheaper, smaller, and less precise ones for a couple hundred bucks. If you can't spring for the granite square, cast iron squares are also used, or if you want to upgrade to the cutting edge of calibration technology, you can also buy newfangled ceramic squares -- basically the same deal, but harder and much lighter (and ranging up to $90,000).