We should have explained it more in details (probably some text) right at the beginning of the game... seems that wasn't clear enough fore many anyway in a nutshell:
...when the panda eat bamboo it grow, the more it eat the more it grow (stop eating and it shrink over time). A bigger panda make it easier to reach higher ground, beat the baddies allows it to push crates etc... but makes it harder to avoid traps, stay on moving platforms etc...