Sometimes when you complete a clue in a puzzle in the main game, you'll find a Bonus Puzzle.
Select the 'Bonus Puzzles' button at the top of the home screen to view the Bonus Puzzles you've found so far.
Bonus Puzzles take time to unlock. Only one puzzle can be in the process of unlocking at a time. If you don't want to wait, you can also use tokens to complete the unlocking process immediately.
You can have up to four Bonus Puzzles available to play at one time. Any further bonus puzzles you find while all four slots are occupied are saved to you collection. Once you complete a bonus puzzle, the slot will be freed up for the next bonus puzzle from your collection.
The Bonus Puzzles screen also shows how many of the puzzles you've found so far (and the total that are available to be found in the game), and how many you've completed.