Power Jump is a badge that allows Mario to use Power Jump, which uses 2 FP. It is an upgraded version of the regular Jump.
In Paper Mario, it is considered a powerful badge, but not as strong as the Mega Jump badge. It is found in Goomba Village when Goombario's grandfather, Goompa, gives it to Mario.
In Paper Mario: The Thousand-Year Door, the badge allows Mario to jump on an enemy using a lot of Attack power. It can be purchased at the Lovely Howz of Badges for 50 coins. It can also be traded from the Pianta Parlor for 34 Piantas after getting the Special Card. It uses 1 BP.