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Pokemon and Humans are basically like Angels and Humans/Lillins from Evangelion.
While humans and normal animals are carbon-based lifeforms, all Pokemon are made up of Infinite Energy (what is used to power the Kalos Ultimate Weapon or Devon was using to reroute the meteor). This Infinite Energy persists everywhere in the Pokemon universe, which Pokemon use for attacks (creating infinite water), their appearances (all pokemon share the same DNA from Mew and with humans, but their different appearances comes from how they express themselves using that energy), their typing (certain Pokemon have an aptitude for certain types), and their growth.
To elaborate, levels are a way of measuring the Pokemon's skill at manipulating Infinite Energy, moves are recorded manipulations and PP is how often they can repeat these manipulations before being too exhausted to do so. Levels may also mark how much energy the pokemon has been absorbed during manipulation and manipulated (attacked), and Evolution may occur once enough energy has been stored.
Should I go on?