There are several typed of Hints, which each work a bit differently:

Regular Hint - Identifies the first letter of the shortest unfound word.

Picker Hint - Allows you to reveal a letter of your choosing. Tap on one of the letter boxes of an unfound word to pick the letter to reveal. Tapping the hint button again instead of choosing the letter will let you return to the game instead of using a hint.

Hints only work on required words.