Pouteria sapota, mamey sapote, is native to Central America, naturally ranging from southern Mexico to southern Costa Rica.
Wait for the fruit to get slightly soft to touch. Cut open, get rid of the fat black seed, scoop the flesh out an eat. In taste, this is like the chikoo fruit in India, but somewhat fibrous. These fruits are very expensive in Bay Area but if I get it again, I will try milkshake, which is apparently a Cuban favorite.