The basic idea is "burn baby, burn!"

Self-cleaning ovens use an approximately 900 degrees Fahrenheit (482 degrees Celsius) temperature cycle to burn off spills leftover from baking, without the use of any chemicals. A self-cleaning oven is designed with a mechanical interlock (patented in 1982) to keep the oven door locked and closed during and soon after the high-temperature cleaning cycle, which can be approximately three hours. The door stays locked to prevent burn injuries. You can open the oven door after the oven cools to approximately 600 F (315 C).

chef taking food from oven
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Self-cleaning ovens have the added benefit of more insulation, which helps the energy efficiency for regular baking.
If baking spills are not wiped up after baking, there may be some smoke during an oven cleaning cycle. It is a good idea to remove any pets from the area when running the oven's self-cleaning cycle. There have been reports of oven-heated Teflon-coated items releasing odorless fumes deadly to birds.

Self-cleaning ovens have the added benefit of more insulation, which helps the energy efficiency for regular baking. This is similar in concept to an increased R-factor for home insulation.

You will also save energy costs by using the self-cleaning cycle right after baking, to make use of the already partially heated oven.