Everyone in your party has a vocation, the protagonist included, and these determine what spells and abilities they are capable of learning, how their attributes will increase, and what equipment they can use. Make a point of trying out all sorts of vocations to see which combination suits you best. DQ III HD-2D Remake also features an all-new vocation: the monster wrangler. They know more than most about monsters, and will help you befriend any creatures you find who look lonesome.
Allies with this unconventional vocation do battle with an array of monstrous abilities. Not only can they learn attacks which deal damage to multiple enemies at once, they are also capable of using abilities which heal their companions.
Having a monster wrangler in your party will stop friendly monsters from fleeing when you approach. They also possess the Animal Instinct ability which allows them to sense how many cordial critters are nearby. Monster wranglers also learn more abilities in line with the number of monsters you've saved.