Spanish explorers happened on to the Allspice plant in Jamaica in the beginning of the 16th century. The Spaniards thought the fruits look like pepper so they gave it the name of Jamaican Pepper and pimento from the word "pimienta", Spanish for peppercorn.
The green Allspice berries are picked and then dried. They are very high in eugenol which is the main flavoring substance of the berry.
Allspice is available as whole berries or ground. Grinding your own whole berries will provide the most intense flavor and the longest shelf life.