As you battle alongside your monstie you'll gain kinship, which will eventually result in you being able to ride your monstie, so you can act as a single unit. This will allow you to deal way more damage, and as your kinship increases even further, it will allow for devastating levelled up attacks. Against standard enemies you probably won't need this mechanic at all, but when stronger monsties and bosses pop up, riding will give you the damage boost you need to win.