It can only allow so much current to flow thru it, and can only reduce the current flowing to some minimal amount. The two extremes are called saturation and cutoff respectively. But for digital operation, it is these endpoints wheich are used. That is, for digital purposes the transistor is either 'off' or 'on'. Hence, the transistor used in this way has two operating modes, or 'st ates'.
Binary systems seem very trite to the beginner, and they are in some ways.
But if we want to utilize tra nsistors in digital systems we must 'go' with what we have. Each transistor can represent one 'place' in our nu mbering system. Of course, we will need many of these transistor 'places' if we want to count very high. Since each transistor can have two states we need to come up with the symbols to use for each state. The obvious is to use 0 and 1.