In Super Mario RPG: Legend of the Seven Stars, FP, or Flower Points, are similar to Magic points or Mana points in other RPG games such as Final Fantasy. Mario and his party use FP to perform special moves, such as Mario's Super Jump attack and Mallow's Psychopath.
Mario's party uses a variety of syrups to replenish their FP supply, as well as Flower Jars and Flower Boxes to increase their total FP rating.
While adventuring, there are several ways to replenish the party's FP count. One way is to sleep in an Inn; while finding a Mushroom will refill your FP supply and your party's HP, or Health Points.