Allspice is not a combination of spices, rather it is the dried berry of the allspice tree, also known as the pimento tree (no relation to the sweet pepper pimento). The pimento tree is native to the West Indies and Central America.
The allspice berry tastes like a combination of cinnamon, cloves, and nutmeg, thus leading to the confusion that it is a melange of spices. Jamaica is the largest producer of allspice and the Jamaican product is considered superior to those from other countries such as Mexico, Honduras and Guatamala.
Allspice can be purchased ground or as whole berries (preferred). It can be used in baking (best known as the "secret inredient" in pumpkin pie, savory dishes such as jerk chicken, and with vegetables, especially winter vegetables such as turnips and squash.