In Dr. Viktor’s laboratory, you can find the section “Rank Up”.

Here you can use the Cells acquired to push your Monsters beyond their natural maximum level.

For Example:

A Monster could be maxed out to level 100, but Rank him up and he can hit 130.

After Ranking up a Monster you will find that they require more Cells to reach that next rank, with a maximum of a level 5 rank.