the Higher The Level, The Easier It Is To Train. For Example If Your Pet Is Level 20, Your Pets Strength,Movement, Defens Can Be 40
If you're training at the training school, or the swashbuckling academy, to train your other stats such as health and strength, you'll need a high enough level, like concussion said. Within ranges of level, training cost varies. The higher the range, the more expensive it gets. Having a high enough level also lets you learn different faerie abilities, some of which are very useful in the battledome. A high level alone doesn't equal a strong neopet, but it definitely helps.
level is there to train stats thats about it, they should make the battledome better graphic instead of just text base =D