The pet score in Hypixel Skyblock represents the collection of unique pets by a player. This score is influenced by the rarity of the pets, with higher rarity pets yielding a higher score. Achieving a max level with a pet contributes an additional point to the pet score. Rewards for accumulating pet score include extra Magic Find and 3 SkyBlock XP per point. However, only the highest rarity of a specific pet contributes to the score, not multiple rarities of the same pet.