Binary is a number system that uses only two digits, 0 and 1, rather than the ten digits used in the decimal system. Each digit in a binary number represents a power of two. Most digital information is stored using binary numbers, which are longer than decimal numbers but can only use the digits 0 and 1. The document provides an example of converting the decimal number 37 to its binary equivalent of 100101 and vice versa. It also shows how binary addition and subtraction works through an example of converting 104 to its binary form of 1101000.