To think up something means to create or invent it in your mind. When you think up an idea, you're coming up with something new through imagination and mental effort.

You might think up an excuse for why you forgot your homework, think up a story to write for English class, or think up a clever solution to a tricky math problem. Scientists think up hypotheses to test. Engineers think up designs for new machines. Your friend might think up a fun game to play at recess.

The phrase suggests active mental work rather than just remembering something that already exists. You're not recalling a fact you learned or repeating someone else's idea. You're generating something original, even if it's just original to you. When your teacher asks you to think up three questions about the chapter you read, she wants you to create your own questions, not copy them from the textbook.

Sometimes people think up great ideas quickly, and sometimes it takes time and effort. Either way, thinking up involves using your imagination and creativity to produce something that wasn't there before.