Something which perplexes or embarrasses; especially, a toy or a problem contrived for testing ingenuity; also, something exhibiting marvelous skill in making
You can describe a person or thing that is hard to understand as a puzzle. Data from Voyager II has presented astronomers with a puzzle about why our outermost planet exists = mystery. to confuse someone or make them feel slightly anxious because they do not understand something
a toy that tests your ingenuity a particularly baffling problem that is said to have a correct solution; "he loved to solve chessmate puzzles"; "that's a real puzzler"
be uncertain about; think about without fully understanding or being able to decide; "We puzzled over her sudden departure
If you puzzle over something, you try hard to think of the answer to it or the explanation for it. In rehearsing Shakespeare, I puzzle over the complexities of his verse and prose