Tornadoes are most common in "Tornado Alley," shown on the map,  particularly in spring and summer. They're also relatively common in Alabama,  Arkansas, Florida, Georgia, Illinois, Indiana, Iowa, Kansas, Louisiana,  Mississippi, Missouri, Nebraska, Oklahoma, South Dakota, and Texas.

The conditions that produce a "tornadic thunderstorm" (a storm that produces  a tornado) exist when moist, warm air gets trapped beneath a stable layer of  cold, dry air by an intervening layer of warm, dry air. This stratified sandwich  of air is called an inversion. 

If the cap is disturbed by a front or disturbances in the upper atmosphere,  the warm, moist air can rise and punch through the stable air that was holding  it down. The warm air will start to spiral upward, as latent heat is released  when the moisture it holds condenses. Aided by different winds at different  levels of the atmosphere, the rotating updraft gains velocity. That, much  simplified, is the origin of a tornado.