Symbolism, Imagery, Allegory
"The Leopard" is not only the name of this book, but also the symbol of the House of Salina, Prince Fabrizio's aristocratic family. The leopard means a whole bunch of things, but on a general level, it symbolizes the power and gracefulness of the Italian aristocracy. It's a symbol that goes all the way back to the Etruscans, who were some of the first inhabitants of Sicily. At one point, we hear that there is a stone leopard above the door of Fabrizio's country home: "Over the great solid but sagging door, a stone Leopard pranced, in spite of legs broken off by flung stones" (2.4). As you can imagine, the fact that this leopard's legs have been broken off doesn't bode well for the future of the Salinas or the Italian aristocracy in general.
Later in the novel, Fabrizio refers to himself directly as a leopard, saying, "We were the Leopards, the Lions; those who'll take our place will be little jackals, hyenas" (4.104). In other words, he's saying that the old world of Sicily was once run by powerful, graceful aristocrats. The modern Italy, though, is going to be run by people who know how to pick every last bit of meat off of a good deal. They'll be cheaters, swindlers, and scavengers, like jackals and hyenas.
In the final scene of The Leopard, Fabrizio's daughter Concetta (now an old woman) catches something out of the corner of her eye:
During the flight down from the window his form recomposed itself for an instant in the air one could have seen dancing a quadruped with long whiskers, and its right foreleg seemed to be raised in imprecation. Then all found peace in a heap of livid dust. (8.56)
She thinks that she sees a running leopard, but then she realizes that it's just her old stuffed dog Bendicò getting tossed in the garbage. This little detail basically sums up what we've seen throughout this entire book: the grace and power of the Salina family (symbolized by a leopard) is getting thrown into the trash bin of history along with the rest of Sicily's aristocratic past.