Pimenta dioica 

Description: Allspice, also known as Jamaica pepper, myrtle pepper, pimenta, or pimento, is the dried unripe berry of Pimenta dioica, a midcanopy tree native to the Greater Antilles, Southern Mexico, and Central America, now cultivated in many warm parts of the world. The name allspice was coined as early as 1621 by the English, who valued it as a spice that combined the flavours of cinnamon, nutmeg, and clove. 

Flowering and Fruiting: Flowers start during the monsoon season. 

Economic Importance: Pimenta dioica has been used for a variety of human endeavors, such as in perfumery industry, food spice, as a natural pesticide, and in folk medicine.  

Reference: https://en.wikipedia.org/wiki/Allspice