I know that your Pokémon can sometimes avoid an attack and live on one HP when it should have fainted, but other than that, what else can having high affection do?
At affection level 2 and higher, a Pokémon will gain 1.2 times the normal experience from battles. At affection level 3 and higher, a Pokémon may endure attacks that could otherwise make it faint and survive with 1 HP (including confusion damage). This can activate multiple times per turn. At affection level 4 and higher, a Pokémon can sometimes: Avoid attacks, even when they have 100% accuracy. This can activate multiple times per turn. Shake off status conditions at the end of the turn. At affection level 5 and higher, a Pokémon's chance of scoring a critical hit is doubled. Pokémon with maximum affection may also receive the Best Friends Ribbon. In Pokémon Omega Ruby and Alpha Sapphire, a Pokémon with increased affection will need fewer Pokéblocks to max out its condition stats.
At affection level 2 and higher, a Pokémon will gain 1.2 times the normal experience from battles.
At affection level 3 and higher, a Pokémon may endure attacks that could otherwise make it faint and survive with 1 HP (including confusion damage). This can activate multiple times per turn.
At affection level 4 and higher, a Pokémon can sometimes: Avoid attacks, even when they have 100% accuracy. This can activate multiple times per turn. Shake off status conditions at the end of the turn.
At affection level 5 and higher, a Pokémon's chance of scoring a critical hit is doubled. Pokémon with maximum affection may also receive the Best Friends Ribbon. In Pokémon Omega Ruby and Alpha Sapphire, a Pokémon with increased affection will need fewer Pokéblocks to max out its condition stats.
There are places where Affection benefits do not take place, like online battles. Eevee evolves into Sylveon with two hearts of Affection. There are also several quotes that only appear when Affection bonuses happen in battle.
Source
Hope I helped!
