"Most Serene" is an appellative often appropriated by sovereign republics in Italy. Venice's primary medieval rival, Genoa, was also sometimes called, "Serenissima Repubblica di Genoa," and the Republic of San Marino is still officially called, "Serenissima Repubblica di San Marino" to this day. The appellative was also sometimes used by prince-electors of the Holy Roman Empire, who would be called "His Serene Highness;" as would grand dukes and sovereign princes.
Of course, the Republic of Venice was the longest-lived of the Italian republics, and in addition to being one of the most important states on the Italian peninsula, was also a major european power between the fourteenth and sixteenth centuries. Thus, the world "Serenissima" came to become shorthand for the Republic.