Binary is the language used by computers to represent numbers using only 0s and 1s. It uses a base-2 system where each place value is double the previous (1, 2, 4, 8, etc.), unlike the base-10 decimal system used for everyday numbers. To write a number like 9 in binary, you add place values (8 + 1) to get to the target number using only 0s and 1s, without being able to use other numbers like 4 or 2 as in incorrect examples. Understanding binary allows calculating the size of computer files by counting the number of bits (0s and 1s).