Pink peppercorns (a misnomer, as they are unrelated to true peppercorns) come from two plants native to South America: the Peruvian peppertree (Schinus molle) and Brazilian peppertree (Schinus terebinthifolius).
Pepper tree (aka Schinus molle) extremely medicinal tree. pink (redish) peppercorn is used in cooking, although different from black peppercorn. Treats depression, leaves can be burned to ward away negative energy, clears chest colds, lowers blood pressure, relieves pain...and the list goes on.
My fiance and I were just talking about peppercorns, the kind you put in a grinder for the table. I have no idea how they grow and the pictures I've found are fascinating. I'd love to grow them (tree? bush? no idea) but I need to research a bit more. Seems like something that could be very useful and giftable too.