Experience Points or EXP serve only to state how many winning battles a monster has taken part in. A monsters level is actually determined by it's Hit Points.
Unlike HP, EXP is not capped at 99, currently the EXP cap is unknown however it is assumed to be 255 since it likely only occupies one byte.
It is possible EXP somehow effects a monsters preformance, though no evidence that it does has been found.
According to Flux in the instruction manual getting to 30 experience will trigger the level up, this is completely false.