A switch found on some tube amplifiers that changes how the tubes are configured, and reduces the efficiency of tube operation, reducing the power output of the amplifier. A triode tube has a control grid (signal in), a plate (signal out), and a cathode. A pentode adds two more components: a screen grid and a suppressor grid; these make the tube more efficient and increase power output. With pentode/triode switching, the grids are effectively removed from the circuit, reducing the efficiency and dropping the power output roughly in half — thus the use of “half-power switch” as a frequent synonym.
Note that dropping the power in half does not reduce the amp’s volume or SPL by 50%. The amount the volume drops depends on how hard the power tubes are being driven and other factors. However, a triode setting for an amp may result in the power tubes breaking up at lower volumes, and may also change the tonal and response characteristics of the amp to a certain extent.