To puzzle over something is to try to understand or solve it. Picture someone struggling with a jigsaw puzzle, trying to figure out how all those tiny pieces fit together to form an image. That person is puzzling over a puzzle!
When something puzzles you, it confuses and mystifies you. New technology might continually puzzle your grandfather, while your grandmother is quick to figure it out. When you puzzle over a difficult book or the instructions to your new TV, it's like you're trying to piece together a tricky puzzle — a challenging game or problem. The classic puzzle is a jigsaw puzzle, a picture that's split into small, oddly-shaped pieces you need to reassemble into a whole. There are also logic puzzles, crossword puzzles, and mechanical puzzles like a Rubik's Cube. If you can't figure a person out, you can also call them a puzzle.