Granita is a Sicilian, dairy-free frozen dessert with ice granules in it.
It is compared to a grainy gelato or sorbet. Your tongue should be able to feel the ice crystals in it.
On hot summer mornings, some Sicilians will have it for breakfast, served in a glass along with a spoon to eat it, and a brioche bun. You can eat the brioche and granita in alternating bites, or, split the brioche open and spoon the granita onto it, or, dip pieces of the brioche into the granita.
The flavouring should be subtle. Lemon is one of the most popular flavours. Other popular flavours include orange, strawberry, mulberries (gelso nero), mint, jasmine, rose-petal, pistachio and almond (because bitter almonds are used, a truer almond taste comes through.)
The coarseness can vary, and it can be drier or slushier, depending on where in Sicily it is made. On the east coast of Sicily, it tends to be smooth. On the west coast, and in Palermo on the north-west coast, it is quite coarse. Coarse ones are only occasionally stirred while being frozen. Smooth ones have likely been made in a machine such as a gelato machine.
The base ingredients of Granita are very simple: sugar, water, and a flavoured liquid such as a fruit juice. In addition to fruit-flavoured ones, there are also coffee and liqueur flavoured ones. Chocolate granita is made in the city of Catania, Sicily.  Coffee-flavoured is popular in Messina. The mixture is then frozen.
To serve, the top of the frozen mixture is scraped to cause it to “shave off” in layers of crystals. You don’t want it to freeze completely solid, though, like one big ice cube, or you won’t be able to scrape it, unless you are going to buy a specialized ice scraper kitchen tool.
At home in Sicily, some people make Granita by freezing the mixture, then using a hand blender to crush it for serving. 
On the island of Salina, in the Aeolian Islands, Granita is topped with whipped cream (except the lemon flavoured Granita.)
Granita started being made in the late 1600s, at the same time that chilled desserts started appearing in other parts of Italy.
 In 2009, Faith Willinger noted that Caffe Sicilia, in Noto, was serving chocolate, moscato grape and even spicy fig flavours.
 Torre, Phil. Quest for Sicilian Granita. New York: italianchef.com. 2004. Retrieved September 2010 from http://www.italianchef.com/questgranita.html
Hamaker, Nichole. Granita and Brioche for Breakfast. “Pinch my Salt” blog. 5 July 2007. Retrieved September 2010 from http://pinchmysalt.com/2007/07/05/granita-and-brioche-for-breakfast/
Steingarten, Jeffrey. The man who ate everything. Toronto, Canada: Random House. 1997. Pages 361 – 380.
Willinger, Faith. Granita: Sicily’s Slushy Treat. The Atlantic Magazine. 6 July 2009.