Wikipedia
A hydrocyclone (often referred to by the shortened form cyclone) is a device to classify, separate or sort particles in a liquid suspension based on the ratio of their centripetal force to fluid resistance. This ratio is high for dense (where separation by density is required) and coarse (where separation by size is required) particles, and low for light and fine particles. Hydrocyclones also find application in the separation of liquids of different densities.
A different description: A hydrocyclone is a mechanical device designed to reduce or increase the concentration of a dispersed phase, solid, liquid or gas of different density, by means of centripetal forces or centrifugal forces within a vortex.
The mixture is injected into the hydrocyclone in such a way as to create the vortex and, depending upon the relative densities of the two phases, the centrifugal acceleration will cause the dispersed phase to move away from or towards the central core of the vortex.
A hydrocyclone will normally have a cylindrical section at the top where liquid is being fed tangentially, and a conical base. The angle, and hence length of the conical section, plays a role in determining operating characteristics.