The map above shows the extent of both Carthaginian and Roman territory in 218 B.C. - just prior to the 2nd Punic War. In the Red Corner we have Rome, occupying much - but not all - of modern day Italy. In the Purple Corner we have Carthage, occupying just about everywhere else.
Carthage started life as a Phoenician colony, but it very soon came into its own. Its people were a mercantile people, creating and controlling the trade networks of the western Mediterranean. (1) Their influence stretched along the coast of north Africa and into Spain, Sardinia, and Sicily. If you needed carpets, rugs, dyes, jewellery, pottery, lamps, tapestry, timber, hides, food, or wine, chances are that there was a Carthaginian merchant who could get them for you. This trade was protected by Carthaginian control of the sea - they had a formidable navy - and it was this control which brought Carthage into conflict with others. (2)
Carthage and Conflict
First Punic War
It was Carthage's interest in Sicily which worried people most. When Rome was still young, Sicily and southern Italy were colonised by the Greeks, and for centuries the Greeks and Carthaginians fought on and off for control of the island. Initially, Rome stayed out of it, even going so far as to sign two treaties with the Carthaginians saying as much. When southern Italy became Roman, however, they realised that Carthage was a little too close for comfort. Under the pretence of helping their 'friends' in Sicily, Rome declared war on Carthage - thus began the First Punic War. (3)
When you think of the Roman military you think of armour clad soldiers with sword and spear and shield - a Roman navy doesn't really spring to mind. In 264 B.C. this vision is especially true, as the Romans had very few ships indeed. Needless to say, when their handful of ships came up against the Carthaginian fleet, they were destroyed. However, if nothing else, the Romans were quick to adapt; realising that their strength lay in their infantry, they engineered and equipped their boats with a corvus. The corvus, meaning 'crow', was a platform which would swing down and pierce the enemy's deck (like a crow's beak, hence the name); this let the Romans turn naval combat, with which they struggled, into infantry combat, at which they excelled. By 241 B.C. Carthage was defeated, and sent packing back to Africa. Forced to give up valuable territories to Rome, and made to pay 96 tonnes of silver to Rome, Carthage was humiliated.
Second Punic War
With a fortune to pay and none of Sicily's resources to pay it with, Carthage turned its eyes towards Spain, a country rich in silver and gold. Spain allowed the Carthaginians to reclaim some of its lost pride, but many still had nothing but contempt for the Romans. According to Livy, one such person was Hannibal Barca; as a child, "(Hannibal swore), with his hand laid on the (sacrificial) victim that as soon as he possibly could he would show himself the enemy of Rome". (4) This account is doubtless made up, but it illustrates very nicely the point that with Carthage on the rise once more, another clash with the Romans was almost inevitable.
In 218 B.C., with Carthage once again getting too close to Roman interests, Rome declared war. By this stage, however, Hannibal was already approaching the Alps with some tens of thousands of soldiers (and 37 war elephants), ready to descend on Italy. Rome was in trouble.
Footnotes1) Polybius, 6.56.1
2) Polybius, 6.52.1
3) Polybius, 1.10.1
4) Livy, 21.1