I remember having to learn this sentence at school, it demonstrated a rule in Latin, a very important rule, one which I have completely forgotten. But let's start with a quick explanation for the ones who weren't force-fed Latin grammar in their childhood.
Delenda Est Carthago, Carthage must be destroyed, or more exactly: "Ceterum censeo Carthaginem esse delendam" which translates as "And therefore, I conclude that Carthage must be destroyed", was the motto of arch-conservative Roman Senator Marcus Porcius Cato. He is generally referred to as Cato the Elder to distinguish him from his grandson of the same name, who also rose to prominence in Roman history and is known as the Younger.
Cato was relentless. He used this motto, this tagline, everywhere.
Rome had already fought two wars against Carthage, most of us are vaguely familiar with the second of these during which Hannibal crossed the Alps with his elephants. Cato, veteran of both wars, was appointed an ambassador to Carthage. He was astonished, and appalled, at what he saw there.
He saw the mighty harbour with wharves piled with the wealth of many countries; the marketplace with abundant food from many parts of the world, warehouses filled with spices, rich and rare merchandise, gold, precious oils and ivory. He saw the graceful houses with their sculpted gardens, the towering public buildings, the massive city walls; the wealth of Carthage was great and wonderful. And he was sickened.
Cato understood that two expansionist empires could not co-exist. The world would be ruled by one power or the other, Imperialist Rome with her armies or the commercial empire of the Phoenicians, and he saw but one way to ensure Rome would triumph. Rome must move fast and strike first with all her force, a pre-emptive strike, Carthage must be destroyed.
It was easy to demonise the Phoenician people as brutish, murderous barbarians. The religion was different, the language and lifestyle different, they looked different. In Carthage, people were somehow less human than those in Rome. The Romans viewed Hannibal himself in mythic terms, as a folk monster, a devourer of children, a cruel and cunning invader who was stopped only by epic courage and perseverance from the vastly morally superior people of Rome.
The only defense, Cato said, was to attack. To destroy it.
Eventually, Cato's persistence paid off, and Rome started the third and final Punic War against her trade rival.
Cato's slogan was implemented in typical thorough-going Roman style. The walls of Carthage were torn down, the city put to the torch, the citizens were sold into slavery and the Senate decreed that no one could live where Carthage once stood. Some stories say the fields were sewn with salt.
In any case, Carthage was destroyed.