From the Super Mario Wiki
A Flower Box is a box of Flowers found in Super Mario RPG: Legend of the Seven Stars. When used, this item increases Mario's maximum Flower Points by five. As such, Flower Boxes are very rare and usually found after defeating an extremely tough boss. In addition to increasing Mario's maximum FP by five points, a Flower Box recovers all of Mario's FP.
A Flower Box must be used on the item screen before Mario's FP is increased, unlike regular Flowers which instantly increase Mario's FP when picked up.