Pets have a number of different stats that can be affected in different ways during gameplay.
Basic stats include your pet's species, sex, age (in days), and fertility. Pets created using a totem are "born" at 10 days old so that they are created as breedable adults. You can change your pet's name at any time from your Territory page. You can change its sex by using a Sex Change Potion.
Fertility determines how likely your pet is to have twins or triplets. There is no such thing as a "failed" breeding, even if your pet's fertility stat is 0.
Battle Stats include your pet's Strength, Speed, Cunning, and Endurance.
PvE and PvP Battling are features that will be released in the future.