Transistors amplify signals by using a small input current to control a larger current from a power supply, creating a larger output signal. This process is similar to how relays operate, where low voltage controls higher voltage. The output gain refers to the amplification of the signal, not the power, which is why it can appear greater than the input. Efficiency in amplifiers is calculated as output power divided by total input power, which remains less than one since the power supply provides more power than what is output. Understanding this distinction clarifies how transistors function in amplification.