Vitality is a stat in EarthBound that determines HP gain. One Vitality point is equal to about 15 HP. It can be increased with capsules. If a character's Vitality increases by a large amount in a level-up, it can be expected their HP will rise a lot. HP will not always rise by 15 for each Vitality point gained in a level up, but it rises to keep the HP-Vitality ratio at 15.