This spiky fruit with white inside is something you won't come across as the grocery store, at least in America. However the Nephelium lappaceum fruit can be as common as an apple in some parts of Southeast Asia. In Malaysia, Philippines, Thailand, and Vietnam you are bound to come across them. You only eat the white fleshy pulp inside.
This spiky fruit may spike your blood sugar and won't offer much in terms of health benefits. How much antioxidants there are in rambutan is disappointing, but not surprising. Similar to lychees and many other white fruits, the edible portion has very little antioxidants.
Research Support, Non-U.S. Gov't: In Vitro Cell-Mediated Antioxidant Protection of Human Erythrocytes by Some Common Tropical Fruits. J Nutr Food Sci. Research Gate 2012