Why Gain is simply the ratio of what comes out of a stage to what goes in, and that ratio can be measured in any of three quantities. Voltage gain compares output voltage to input voltage, current gain compares output current to input current, and power gain compares output power to input power. A transistor amplifier can have gain in all three senses at once, and which one you quote depends on what the circuit is being used for. Gains are often expressed in decibels, where 10 dB of power gain means the output power is 10 times the input power.
Watch out Picking only the voltage ratio is tempting because that is the figure most often quoted for audio and RF stages, but it is just one of the three valid ways to express gain.
Gain = out divided by in, and the pool lets you measure it in volts, amps or watts.