While no one is quite sure why Tornadoes form, there are several prevalent theories. Here is the most popular one, which seems to answer most questions about why Tornadoes form.
1. Large air masses of different temperatures collide. This usually occurs in the form of a Cold Front meeting a large area of warm air.
2. The warm air mass rises above the colder air, due to heat's tendency to rise. As the air rises, it cools and condenses into rain.
3. The rising motion of the warm air causes a large updraft to occur in the atmosphere.
4. At the same time, wind shear (winds that are close to the surface moving slower than winds higher up in the atmosphere) causes the air mass between the surface of the earth and the top of the supercell to rotate.
5. The warm updraft in the atmosphere tilts the air mass on it's end, resulting in a mesocyclone.
6. The next step in the formation of a tornado is dependent on one key factor: the barometric pressure of the air under the mesocyclone. If the air pressure is low enough, then the spinning cloud mass will follow the path of least resistance and reach to the ground. The result is a tornado.
Considering how much study goes into Tornado formation, scientists still do not know very much. For example, they were just recently able to prove that there is a calm area at the center of the cyclone (it was always believed that there was, but never proven). This was proven when a tornado passed within close proximity to a portable Doppler Radar that many scientists take into the field.
Some tornadoes can have Multiple Vortexes. (picture below)