Riddle

A riddle is a type of word puzzle where ambiguous clues to an object or person's identity are offered requiring the reader to puzzle over what the subject is and thereby find the answer.  

They can be presented as a verse (usually rhyming) such as this one in JRR Tolkein's The Hobbit 

Q: “This thing all things devours;
Birds, beasts, trees, flowers;
Gnaws iron, bites steel;
Grinds hard stones to meal;
Slays king, ruins town,
And beats mountain down.”

A: Time.

or phrased as a question as in Lewis Carroll's unanswerable riddle in Alice in Wonderland "Why is a raven like a writing desk?" or Q. What has a face and two hands but no arms or legs? A. A clock!

A Kenning is another type of poem that behaves like a riddle.