Enlightened absolutism combined the idea that monarchs should have absolute power with the ideals of the Enlightenment. People who believed in this believed that monarchs should keep their power, but that they should use that power in ways that were meant to help their people. They were to do so using the ideas of rationality that the Enlightenment promoted.
These were rulers like Frederick the Great of Prussia. He kept the power in the country to himself, but he acted on Enlightenment ideas. For example, he allowed for a great deal of religious freedom. He promoted education and scholarship and allowed those scholars to publish whatever ideas they wanted to. He abolished torture and improved the legal system. All of these actions were taken because he believed (or at least said) that his role was to be a servant to the nation. This was because of the Enlightenment idea of the social contract, in which government was supposed to be used to protect the people and their rights.