The summer kitchen was usually an out-building, but it could be attached to the main house by a breezeway or roof. As the name suggests, it was where cooking was done during the hot summer months. In a day and age when electric ranges and microwave ovens did not exist, the only way to cook food was to have a fire raging in the fireplace (or later coal or coal-oil stove). The heat from the fireplace or stove would cause the inside of the house to be heated even more than it already was because of the climate. The summer kitchen, being outside of the house, kept the heat from the cooking away from the living areas of the house.
The summer kitchen was even used in the winter if there was a lot of baking to be done, such as during a holiday like Christmas or Thanksgiving.
In the diagram below, the summer kitchen is indicated in red.