The significance of a triple peel is the rule in advanced association croquet that defines penalties for a player who runs their ball through the 4-back hoop.
Because conceding a contact in this way creates a good chance of losing the game, players will generally end a break before running 4-back.
This means that it is common for a player to start an all-round break in a position where another ball on the lawn has 4-back as its next hoop.
In recent years the best players have perfected the triple peel, to the extent that leaving a ball at 4-back is considered risky.
The sextuple peel is now considered one of the highest achievements in croquet, performed only by a handful of top international players.