In the Punic Wars, Rome fought against the city-state of Carthage. In those wars, Rome eventually defeated Carthage. They then totally destroyed the city.
Carthage was a city-state that had been established by the Phoenicians. It was located in what is now Tunisia in Northern Africa. Carthage was established by Phoenician traders from Tyre, which was in what is now Lebanon. By 650 BCE, Carthage was independent and it gradually became a major maritime power in the Mediterranean. Centuries later, when Rome became powerful, Carthage controlled areas all along the Mediterranean, reaching even as far as Spain. Rome and Carthage came into conflict as Rome became more powerful. This led to the Punic Wars.
The City State of Carthage.
The modern location is Tunisia.
Carthage, and Rome, were two growing empires, and both were expanding in more or less the same direction, which led to a conflict between the two powers known as the Punic Wars.