A carpenters square isn’t used that often, but can be useful when cuttings rafter or when building stairs. It’s basically a ruler that is bent at a ninety degree angle. This allows you to measure two distances from the same point at the same time to mark a notch. For example, a roof might have a 12/2 pitch, meaning that it rises 2 inches for every 12 inches of run. If you lay a carpenters square down on a rafter and line up one side of the square at the 2-inch mark, and the other side at the 12-inch mark, and trace the square, it will draw a notch which can serve as the birds mouth (note that the size of the notch may need to be adjusted for the size of the wood you are working with). If these terms are confusing, don’t worry, they will make a lot more sense when you start working on your roof.
There is not much to look for in a carpenters square. I do recommend buying an aluminum version like this Empire Laser Carpenter/Framing Square. I have both an aluminum and a steel version that are about the same age, and while my aluminum one looks brand new, my steel one looks like it’s from WWII.