Gain was a measure of the ability of an electronic circuit or amplifier to increase the power or amplitude of a signal. Gain was usually defined as the mean ratio of the signal output of a system to the signal input of the same system.
Captain James T. Kirk asked Lieutenant Uhura to bring up Spock's voice channel with the highest possible gain while attempting to rescue him from the space amoeba. (TOS: "The Immunity Syndrome")
Just prior to the launch of the newly-refitted USS Enterprise from spacedock in the mid-2270s, there was a transporter accident. During the accident, Captain Kirk requested that Starfleet boost the matter gain on the beaming signal. Unfortunately, the ship's transporter lost the patterns of both Commander Sonak and a female crewmember. Both individuals were killed during the beaming process. The fault was attributed to an inactive transporter sensor which had faulty modules. (Star Trek: The Motion Picture)
Commander Worf had Lt. Dax boost the gain on the transporter energizing coils in an attempt to rematerialize Trentin Fala's transporter signal, which had been disrupted by a remat detonator. The gain could not be increased any higher, and Fala died during transport. (DS9: "The Darkness and the Light")