Carthage was a major power in the Mediterranean world for centuries. It was centered in what is now Tunisia and was powerful from around 650 to around 150 BCE. Carthage stopped being important as an independent power after it lost to Rome in the Punic Wars.
Carthage got its start as a colony of the Phoenicians, who lived in the area of what is now Lebanon. Because Carthage was sited in a particularly rich area with a good harbor, it came to have more and more power on its own. Carthage became rich and powerful through trading around the Mediterranean.
As Rome grew in power on its own, it came into conflict with Carthage. They fought the Punic Wars, which ended with Rome winning and Carthage becoming part of the Roman Empire.