Enlightened despotism (also called enlightened absolutism) was a form of government that tried to combine an absolute monarchy with the more democratic ideas of the Enlightenment.
Enlightenment thinkers like John Locke held that government existed for the purpose of serving its people. The whole point of government was to protect the rights of the people it ruled. Enlightened despotism tried to combine this idea with the idea that monarchs should have absolute power. Under the idea of enlightened despotism, rulers tried to use their absolute power for the good of their people. They were supposed to rule in ways that would help the people rather than simply trying to pursue their own desires.
In this way, enlightened despotism was an attempt to merge ideas of the Enlightenment with ideas of absolute monarchy.