What causes a mesocyclone to form within a thunderstorm?

A storm-scale region of rotation, typically around 2-6 miles in diameter and often found in the right rear flank of a supercell (or often on the eastern, or front, flank of an HP storm). The circulation of a mesocyclone covers an area much larger than the tornado that may develop within it.

Properly used, mesocyclone is a radar term; it is defined as a rotation signature appearing on Doppler radar that meets specific criteria for magnitude, vertical depth, and duration. Therefore, a mesocyclone should not be considered a visually-observable phenomenon (although visual evidence of rotation, such as curved inflow bands, may imply the presence of a mesocyclone).

The Cause of a mesocyclone is wind shear. Wind Shear causes parcells of air to rotate horizantially, then a updraft form which makes the horizantally rotating air to become vertical.

TYpically strong vertical motion, good airmass convergence (a point where warm and cold air collide), cold air aloft, and Wind Shear (Jet stream Energy).