The coffee fruit, called coffee cherries or coffee berries, is edible raw and tastes sweet:
http://www.youtube.com/watch?v=zIbtsck6yHo

Hot coffee beverage is made from the seeds of the coffee fruit, which are bitter and essentially inedible, though some people suck them for the caffeine. Coffee cherries apparently spoil too rapidly to make them a marketable fruit, but they are made into juice that is sold commercially: http://edible-oddities.blogspot.com/2009/03/coffee-berry-juice.html