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.
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")