From SKYbrary Wiki
A mesocyclone is a vortex of air, approximately 2 to 10 miles in diameter, within a convective storm. In a mesocyclone, air rises and rotates around a vertical axis, usually in the same direction as low pressure systems. They are most often associated with a localised low-pressure region within a severe thunderstorm. Such storms can feature strong surface winds and severe hail. Mesocyclones often occur together with updrafts in supercells, where tornadoes may form.
Mesocyclones are believed to form when strong changes of wind speed and/or direction with height ('wind shear') sets parts of the lower atmosphere spinning in invisible tube-like rolls. The convective updraft of a thunderstorm is then thought to draw up this spinning air, tilting the rolls' orientation upward (from parallel to the ground to perpendicular) and causing the entire updraft to rotate as a vertical column.