The allspice name derives from the belief that the berries incorporate several spices.
The leaves also carry some of the essential oils and is used in cooking.
Because of the heavy demand for allspice branches to make aromatic walking sticks in England,
the native pimento groves in Jamaica were almost decimated.
They have since recovered and Jamaica remains a main supplier of this spice.

Description from McCormick Spices
Allspice is the dried, unripened fruit of a small evergreen tree, the Pimenta Dioica.
The fruit is a pea-sized berry which is sundried to a reddish-brown color.
Pimento is called Allspice because its flavor suggests a blend of cloves, cinnamon and nutmeg.