Battle Stats are elements which determine major aspects in the battle systems in the series.
HP (short for Hit Points) determines how much damage a party member can receive before fainting. Their remaining HP is restricted to a maximum value as well. Using certain skills require some of the party member's HP to be used.
SP is a value necessary for party members to use skills. Casting those skills will use up their limited supply of SP in the process. Similarly to HP, their remaining SP is restricted to a maximum value.
Agility (俊敏さ, Shunbin-sa)?, or Ag (速, Haya)? mainly determines the turn order between entities, with faster characters acting earlier. Additionally, it affects the party member's hit accuracy and evasion to enemy attacks.