Powdered sugar, also called confectioner's sugar or icing sugar, is finely ground sugar. It usually contains some anti-caking agent (usually corn starch, potato starch or tricalcium phosphate) to prevent clumping. It's available in many degress of fineness: xxx, xxxx and 10x. The finer particles absorb more moisture which results in caking.
It's possible to make powdered sugar at home using a coffee grinder or a mortar and pestle. It is primarily used to make icing or frosting on cake, or dusted over baked goods.