Rome was trying to grow and gain power through war. They had a large amount of land that consisted of the whole Italian peninsula but they wanted more land.
Carthage had a large amount of land in their possession. They were very powerful and capable of controlling that much land. The only problem was that because they had so much land, there were civilization like Rome that wanted it for themselves.
In The first punic war, it was mostly a naval battle between Carthage and Rome. Although Carthage was strong when it came to naval battles, the Romans outmsarted them by converting them to land battles and won the first punic war.
Hannibal Barca was the commander of the Carthaginian army in the second punic war and chose to send his men and elephants through the snowy alps to directly attack the Romans. The Carthaginians ended up winning the second war.
After the second punic war, Carthage was a small city that doesn't have much land or power anymore. The Romans however, still thought that they could rebuild and come back which started the third punic war. So they burned what remained of the city of Carthage
Rome won two wars and wiped Carthage off of the face of the earth. They took over all of the land that had once been Carthage’s and became an ancient world power.