The value of amplification that a signal obtains in passage through an amplifying stage or system.
In electronics and audio gain is a unit of measurement used to mean the ratio of a signal output of a system to the signal input of the system. Gain is a term most commonly associated with amplifiers.
An increase in signal power, voltage, or current by an amplifier, expressed as the ratio of output to input. Also called amplification.
The amount of amplification (voltage, current or power) of an audio signal, usually express in units of dB (i.e., the ratio of the output level to the input level). For example, amplifying a voltage signal by a factor of two is stated as a voltage gain increase of 6 dB.
Amplification factors are usually expressed in terms of power. 
The decibel (dB), a logarithmic unit, is the most common way of quantifying the gain of an amplifier. For power, doubling the signal strength (an output-to-input power ratio of 2:1) translates into a gain of 3 dB; a tenfold increase in power (output-to-input ratio of 10:1) equals a gain of 10 dB; a hundredfold increase in power (output-to-input ratio of 100:1) represents 20 dB gain. If the output power is less than the input power, the amplification factor in decibels is negative. If the output-to-input signal power ratio is 1:1, then the amplification factor is 0 dB.