A "discrete" signal can only have a one of a fixed number of values, rather than a continuous value like real numbers. If that fixed number is two then we say that we have a binary system, or a binary signal. It is convenient to describe these states as 0 and 1, but we could also call them "on" and "off" or "true" and "false".
It is possible to have three distinct logic values. Such a system or signal is referred to as being ternary. Computing systems using ternary logic have been built but binary systems are clearly dominant today.
In communications systems it is possible to define many more "states", or discrete values, that can be transmitted. These are usually called "symbols" and systems with 16 or more discrete states are common.