Combat: This raises the critical hit ratio.
Stabality: This has no public use yet.
Attitude: This has no public use yet.
Medicine: This increases the amount of HP gained, using Potions only.
Ambition: This has no public use yet.
Heart: This increases the happiness and happiness gained, of a Pokémon caught or owned.
The higher this rating, the more your character effects game play.
Lit stars also mean most gains, less gains, increases or decreases, depending on the effect happening, I.E. Heart, the higher the rating, the more happiness a Pokémon gains, walking around... But, reduces less, up on fainting.