This apparantly is a gain, which, according to "The American Heritage Dictionary of the English Language" is "a notch or mortise cut into a board to receive another part [origin unknown]." American woodworking texts from the turn of the twentieth century use this term. I do not find it used in English woodworking texts.
Its most common usage in the literature relates to the housing or recess made for a hinge leaf. Its made with a knife, chisel and router plane.