There are a total of three Toad Stamps on the front cover of each Episode book. Successfully complete the indicated task to unlock the corresponding stamp.

First Toad Stamp: Successfully complete the episode.
Glittering Stars: Have all three Toad Stamps, then beat the Challenge Times for each level.
Second Toad Stamp: Collect all gems in the episode.
Third Toad Stamp: Successfully complete all Bonus Challenges and collect all gems in the episode.