Something that is noetic has to do with thinking and reason. If you praise your friend's noetic abilities, you think she's very smart.
Use the adjective noetic to describe intellectual thought, like the triumph of the noetic part of your brain over your instincts. It rhymes with poetic, but unlike the emotional content that is usually associated with poetry, things that are noetic focus on reason. The word traces back to the Greek word for mind or thought, noos.