This is the Petpet training center because the higher the level your petpet is, the stronger it gets. This is really useful and can help your Neopet during battle. Your current Petpet will fight against a computer's Petpet and if your Petpet wins, it moves onto the next level.
When battling, a random opponent will be chosen for you. A level one Petpet will be able to challenge opponents up to three levels greater or weaker than his/her level. This is totally random how difficult the challenger is. Obviously the higher the opponent's level is, the harder the fight will be. As your petpet gains levels it will be able to challenge more opponents and eventually, the evil Dr. Sloth.
Every time your Petpet gets a score of ten, it will gain a level. For example, a level one Petpet who wins his tenth match will become level two and its exp meter in numbers will be set back to 0. Once your petpet gains a level it cannot lose it in the Petpet Battledome, even if it never won a match again. However, a zap from the Petpet Lab Ray can sometimes lower (or raise) your Petpet's level. Awakening the Turmaculus can also cause a rise in level for your Petpet, although you run the risk of your Petpet being eaten by Turmy and being gone for ever.