Most of us are familiar with is A4, which is used in photocopiers and desktop printers. Below is a table of sizes for A4, A3, A2, A1 & A0 listed in mm, cm and inches. Each size is twice the area of the previous size (so A3 is twice the area of A4)
Size A4 has its shortest edge (210mm) doubled to its longest edge of A3 (420mm). A3 has its sharpest edge (297mm) doubled to be the longest edge of A2 (594mm). And similarly up to A0.
Paper is specified in texture and weight. Standard A4 photocopier paper is usually 75gsm or 80gsm. The weight in grams is the actual weight of an A0 sheet of paper.