The Mediterranean Sea was important to the Roman Empire in that it was a vital trade link with other parts of the Empire, especially the Middle East and North Africa. As Rome grew, it needed the grains and other food from the Levant, and African animals were considered status symbols in the Roman royal courts. Thanks to the Phoenicians and the Greeks, the Mediterranean was a well-used waterway and Roman sailors were quite familiar with the weather patterns on it. The Romans referred to it as "their sea" and would not allow competing empires to flourish on it, such as the Greeks and Egyptians. The Mediterranean also connects to other waterways of interest to the Romans such as the Bosporus Straits--this gave the Romans access to the spices and other riches of the East.
Another reason why the Mediterranean was valuable was that Romans would have to cross the Alps to get to the rest of Europe. It was far easier to use trade networks that had been used for centuries on the sea rather than use an overland route.