Mesocyclones form when strong changes of wind speed and/or direction with height ("wind shear") sets parts of the lower part of the atmosphere spinning in invisible tube-like rolls. The convective updraft of a thunderstorm then 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.
As the updraft rotates and ingests cooler moister air from the forward flank downdraft (FFD), it may form a wall cloud, a spinning layer of clouds lowered from ambient storm cloud base under the mid-level mesocyclone. The wall cloud tends to form closer to the center of the mesocyclone. As it descends, a funnel cloud may form near its center. This is the first visible stage of tornadogenesis.
Wind shear (red) sets air spinning (green).
The updraft (blue) 'tips' the spinning air upright.
The updraft then starts rotating.