According to Alan Davidson in the Oxford Companion to Food, (Oxford University Press:Oxford) the appearance of "water ices" is documented to have taken place in Europe in the 17th century around the same time as ice cream. There is some undocumented conjecture that Marco Polo returned to Venice from China in the 13th century and introduced ice cream or water ices to Italy. Further it is not known for sure if water ices were first found in Spain or in Italy. In any event the mixture seemed to have migrated to London at some later, undocumented time.
Granita is akin to but not quite the same as sorbet. The difference being sorbets tend to be smoother and less granular in texture. Both are made with water, a flavoring such as fruit juice or coffee and typically sweetened with sugar.
Granita is typically eaten as a refreshing and light dessert. They can also be used in the same way as one would a sorbet, between meal courses to "cleanse the palate".
Recipes can be found for a myriad of flavors from the traditional coffee to more exotic such as pineapple or champagne.
Stir sugar and coffee until sugar has dissolved. Transfer to a 8 x 13" glass baking dish. Freeze at least 3 hours or up to 8 hours.
Before dinner, scrape frozen coffee into shavings using a fork. When ready to serve spoon coffee shavings into serving dishes. Serve with condensed milk drizzled over top.
A variety of machines are available for making granita in large quantities. On the most part they are used commercially but they can be rented or purchased for home use or parties. Some sellers promote using the machines for making "frozen margaritas" as well. Here are a few sources.