Binary is base 2 number system. It is called base 2 because each digit can only be 2 possible values: 0 and 1. Because decimal also has the digits 0 and 1, a subscript "(2)" is usually added to binary numbers to not confuse people.
Computers work in binary, because it is the simplest way to store information using electricity. A wire can be powered on to represent a 1, or powered off to represent a 0. Large sets of binary numbers can be used by computers to represent other types of information, such as text, songs, or videos.