From the Super Mario Wiki
A Flower Jar increases Mario's maximum Flower Points by three in Super Mario RPG: Legend of the Seven Stars. Flower Jars are often received after defeating boss characters. Additionally, Flower Jars recover all of Mario's FP upon use.
Flower Jars need to be used on the item screen before Mario's maximum FP increases, unlike Flowers, which automatically increases Mario's maximum FP as soon as he picks them up.