It involves separating the "cuttings" (drilled material) from the fluid, allowing it to be recirculated or discharged to the environment.
The drilling fluid needs to have the cuttings removed before being recirculated or discharged, which is achieved by the solids control system attached to the rig.
[2][1] Solids control systems consist of several stages of treatment, removing progressively finer particles from the drilling fluid.
[1] The machines that use this principle are called shale shakers, and consist of a series of vibrating screens that the mud passes over.
[3] An alternate design relies on a rapidly rotating drum, which flings the solids in the drilling fluid to the outside of the cylinder to be drawn off as a thick sludge.