Jamaican pepper (Capsicum frutescens) would have first been brought back to Europe by Christopher Colombus. It looks like the pipper nigrum species (black pepper) but it is a totally different species. It is also known as pili pili.
Taste : Jamaican pepper is a good deal for gourmets. It is sometimes called "allspices". Quite aromatic, it gives to your recipes a whole bunch of flavors (black pepper, nutmeg, cloves, cinnamon...). For a better tasting, it is recommended to grind the peppercorns just before use.