When you manducate carrots, you chew them. Your stiff, formal grandmother might instruct you to manducate your food more slowly.
Use the verb manducate when you need a formal word for eating. Horses manducate mouthfuls of hay and little kids who are new to trick-or-treating might want to manducate each piece of candy as it's dropped in their treat bag on Halloween. While chew is a far more common word than manducate, even masticate is used more often. Manducate is rooted in the Latin manducat-, "chewed," from mandere, "to chew."