Level

Level is one of a Pet's statistics, representing how experienced in combat they are. Level cannot be raised directly, instead it is a function of Experience - as experience reaches certain thresholds, the pet will level up. A Notice is generated on Level up, "(Pet Name) (Pet ID) has levelled up to level #!" A pet's Level can be checked at the Battledome, under Pet Status. Level is also shown in the sidebar, below your Active pet's image.

Levelling up increases a pet's HP and Energy automatically, and grants 5 Pool Points which can be spent on Power, Toughness or Speed. These attribute increases are permanent and cannot be reassigned.

Level in Explore
The levelling mechanic in Explore was very different than the one implemented for Adventure - it was extremely difficult to get the first few levels, but once past the threshold, levelling up was incredibly fast. 20-30 levels an hour was not uncommon. The extremely high levels pets achieved was one of the problems Adventure sought to address, since pets above Lv 100 (and there were many in the 1000+ range) could one hit KO everything with impunity.