Gain is a measure of the ability of an electronic circuit to increase the power or amplitude of a signal. Gain is 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 James T. 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")