Functionally transistors are used in circuits primarily as either switches or amplifiers. As a switch, the transistor is so biased that the input signal causes the transistor to fully saturate or fully turn off. The output then changes from near zero Volts potential to near the bias potential, or vice versa, depending on what type of transistor you are using. As an amplifier, the transistor is so biased that it will linearly amplify a small signal into a larger one. The same transistor can be used for both functions, it is a matter of biasing the transistor properly.
Biasing in the above means placing the right potentials at the collector, emitter and base in the case of a bipolar junction transistor, or the proper potentials at the drain, source and gate of a field effect type transistor. These names refer to the construction of the transistor.