Severe weather can come in all forms. It can be tornadoes, hurricanes, flooding, hail, etc. I believe that this question is asking for the answer to focus on typical thunderstorms which are a type of severe weather.
Thunderstorms develop as a result of air instability, moisture in the atmosphere, and a mechanism that "pushes" the air into further instability. These atmospheric conditions seem simple enough; however, their presence has to be in the right amounts, and that is why thunderstorms typically occur in the same parts of the country.
While severe weather thunderstorms can occur year-round, they typically occur in the afternoon and evenings of spring and summer months. This is because warm, rising air is a key ingredient for the formation of thunderstorms. Spring and summer months have extended daylight hours, and that helps to warm the air itself and the ground. Warm air spreads apart, becomes less dense, and rises. Hills or mountains can help with the rising action. As the air rises, it cools. The evening air helps with the cooling as well, and the warm rising air along with the cooling happening as it rises, gives the air instability. Moisture in the air adds to the instability because the rising air that cools will condense and form clouds full of water vapor and ice crystals which in turn bump into each other to create the static charges necessary for lightning. The final element is the "nudge" required to keep all of this instability in motion, and that final nudge usually comes in the form of a front moving in. The developed storm acts as a boundary/front of its own, and it may "bump" into other regions and help propagate additional storms.