You did not specify the time period that you were referring to, so I am proceeding with the assumption that you are asking about the period from 264 B.C.E. to 133 B.C.E., the period generally recognized as the time of the Roman conquest of the Mediterranean.
Conquering the Mediterranean meant defeating another strong Mediterranean power—Carthage. Carthage was not only located in a very favorable position on the Mediterranean Sea, at one of the tips of northern Africa, but it also used this to its advantage in controlling trade routes across the sea. In fact, Carthage was a massive commercial center, and it essentially monopolized western Mediterranean trade. Around 264 B.C.E., the Romans began to challenge them for supremacy in the Mediterranean, partially because they worried that Carthage may begin to encroach upon their spheres of influence and control. They fought a series of battles which have come to be known as the Punic Wars.
The Romans managed to reap several economic benefits from their victories in these wars. After the First Punic War, they gained full rights to Sicily, and they forced the Carthaginians to pay them an indemnity. They then seized the islands of Sardinia and Corsica, provoking the Second Punic War. From this war, the Romans seized Spain from Carthage and forced Carthage to pay another indemnity, effectively becoming the dominant power in the western Mediterranean. This means that, as I mentioned in the prior paragraph, they now monopolized trade in this region. Eventually, this led the Romans to become more involved in the affairs of the Hellenistic kingdoms in the eastern Mediterranean. In general, the empire then grew and became more expansionist, partially because of the massive economic benefits they could reap through expansion, such as new places of command, spoils of war, and new supplies of slave labor.
For further reading, I would recommend the 9th edition of Western Civilization, edited by Jackson J. Spielvogel. I would also recommend the links below.