The term is supposedly derived from the melting of the two Latin words Dominus (Lord) and Domus (house) through medieval "vulgar" Italian, in the sense that the cathedral is "the house of God". It was also called, in fact, domus Dei, or domus Ecclesiae. Cities with outstanding cathedrals will often refer to it simply as "Il Duomo" or "The Duomo" without regard to the full proper name of the church.
In Architecture, and in Catholicism, the Duomo represents the continuity with the ancient basilica. The term is properly used for the most important church of a town, while the cathedral, (which name comes from cathedra episcopalis) better refers to the bishop's office; apart from this distinction, these words would be perfect synonyms. Curiously, the word has no plural form in Italian, since there cannot be more than one most important church at a time.
Usually a Duomo is highly decorated, often containing notable artworks, and in many cases the buildings themselves are true artworks. Perhaps the best known Duomo is Milan's Duomo di Milano, but cathedrals in other cities have been mentioned in Wikipedia for Alba, Mantua, Nugoro, and Florence's Santa Maria del Fiore. Other notable examples of the type in Italy are in Pisa (the leaning tower is its campanile, bell-tower), in Siena, San Gimignano, Orvieto, Volterra, L'Aquila, Modena, Cittą di Castello, Prato, Naples (and in many other towns).