On older analogue dimmers, this is the way the output curve looks as a result of phase control on a sinewave (how all leading edge triac dimmers work) if no correction is applied to the control input. Note that, at 50% control input, the output is also at 50%. Historically, the majority of dimmers followed this law as other laws required additional circuitry.

Linear, which should strictly be called a Linearising law, can be achieved on older analogue dimmers by applying an inverse S curve so that the output of the dimmer will respond linearly to the control input. On more modern digital dimmers (increasingly prevalent), this is normally the 'default' curve.

Square is usually for Video Cameras, which are more sensitive than the human eye to variations in intensity at high light levels. The square law is intended to compensate for the response curve of the camera, so that the brightness as seen by the camera varies linearly with the control input.

Switch or non-dim keeps the output at 0 until the control passes a set point (normally 50%), where the output then snaps to full.