From the Super Mario Wiki
The Punies are a species of small quadrupedal creatures which resemble insects found in the game Paper Mario: The Thousand-Year Door. They live in The Great Tree located in the Boggly Woods. Mario must use them to defeat a rival clan, the Jabbies, twice in The Great Tree.
The word "Puni" is a pun on the word "puny", meaning "small".
As Mario was exploring Rogueport Sewers for the first time looking for The Thousand-Year Door, he stumbled upon a small insect creature which was, indeed, a Puni. However, it escaped through a small opening, and Mario was unable to interact with it.
Later, after Mario gets the first Crystal Star (the Diamond Star), he goes back to Rogueport Sewers, now with a new ability, which is turning sideways. Luckily for Mario, next to the opening in which the insect had gone through were bars. Mario went through these bars to find out that the insect was just behind them. Mario learns that this insect is named Punio, who tells Mario his homeland, Boggly Woods and primarily The Great Tree, is under attack, and that he needs his help.
The Great Boggly Tree
When Mario reaches The Great Tree through a "secret entrance", he is told by a few Punies, which were all hidden, that their friends have been locked up somewhere in The Great Tree. Upon freeing them, Mario and all the Punies in The Great Tree will attack the Jabbies, the Punies' rivals, who have allied with the Secret Society of the X-Nauts. A total of 101 Punies, including Punio and Petuni, will temporarily join Mario during the events of Chapter 2.
After Mario defeats Lord Crump and the X-Nauts, the Punies will go back to their normal lives, and even make peace with the Jabbies.
Names in other languages