Allspice (also called Jamaica pepper, Kurundu, Myrtle pepper, pimento, allspice berries, or newspice) is a spice which is the dried unripe fruit of the Pimenta dioica plant, a tree native to the West Indies, southern Mexico and Central America.he allspice was named because the flavor of the berry is like a mixture of cloves, cinnamon, and nutmeg. It is used very much in baking, mostly for making mincemeat and mixed pickling spice. It was discovered first by the early Spanish explorers, who mistook it for a type of pepper.