There are 6 main stats: HP, Attack, Defense, Magic, Resist and Speed. All 6 basic stats can be enhanced beyond normal means (leveling up and evolution) and by using Enhancement Stones at the Enhancement Room.
HP indicates the amount of Max health your pet has. Pets lose HP when they take damage in battle.
SPEED indicates the amount of attacks your pet can do in a round compared to the enemy's pet speed. However this does not include the first attack of the battle, this is because that full attack pets should have a chance to strike first, if the first attack was in calculation to speed that means that some speed based pets would not give the full attack based pet a chance to deal damage.
ATTACK indicates the physical damage dealt by your pet. This stat does not mean your basic attack will be stronger, some pets have magic base attacks and some have physical basic attacks, so it gives physical damage type pets a boost and not to magic type pets.
MAGIC indicates the magic damage dealt by your pet. Some physical damage pets have skills that increase their magic attack, this boost only the magic stat the pet have and has nothing to do with the physical damage, so the formula is base damage suppose to be done + base magic damage x skill damage = total damage done in physical and magic damage (that means u deal both physical and magic damage but better focus on one for more damage output
DEF indicates the physical damage reduction your pet has. Defense determines how sturdy your familiar is against physical attacks.
RESIST indicates the magic damage reduction your pet has, it is used to reduce the enemy's magic damage.