People use all kinds of symbols, sounds, colors and body motions to express themselves. These expressions are, in a sense, codes—signals we use to communicate with one another.
Computers use a special code of their own to express the digital information they process. It's called the binary code because it consists of only two symbols—0s and 1s. (The "bi" in "binary" means two.)
Why 0s and 1s? Because those are the only two numbers you need to express the flow of electricity through a transistor. It's either on or it's off. On is 1, off is 0. Everything you say to a computer has to be put in terms of these two numbers.