When purple, they're edible. The single seed in each fruit is relatively large, however, and the few ripe ones I sampled were tart. If not sweetened and made into jelly, perhaps seagrapes are best when overripe; of the many other common names, my favorite has got to be raisin de la mer.
Seagrapes grow on what can be either a large shrub or a small tree in tropical and subtropical climes. The species is very salt-tolerant: From where I found these specimens, the Atlantic was virtually over my shoulder.
(From an autumn 2012 visit)