You can play a puzzle in standard mode (That’s where you move pieces around normally to complete the puzzle). But if you’re looking for an extra challenge you can play a puzzle using a different “game mode.”
Each "game mode" is represented by a symbol, shown during gameplay.
Move pieces normally
Rotate pieces to make them fit
Flip pieces to make them fit
Touch pieces to reveal
Race against the clock
Significantly more pieces than a regular puzzle
Here's a video that explains this further.