Parakarry works for the Post Office in Toad Town, the capital of the Mushroom Kingdom; his boss is the Postmaster. Parakarry tends to be quite clumsy and often loses the letters he is supposed to deliver, and it is also noted in-game that he is rather slow at delivering mail. As such, there are quite a few pieces of undelivered mail scattered across the kingdom. Parakarry's name is a portmanteau of "Paratroopa" (or perhaps the alternate "Parakoopa", as his name features a "K") and the word "carry", as he is a mail carrier whose ability involves carrying Mario.
In Paper Mario: The Thousand-Year Door, Yoshi has the same ability as Parakarry, to carry Mario over gaps that he can't jump over.