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.
One of the main reasons that the sea was important to the development of the Roman Empire was that it was considerable faster and safer than land transportation. Although the Romans were justly famed as road builders, and had a very efficient postal system for government business (the cursus publicus), it could still take two to three months for messages to travel from Rome to provincial capitols. Also, it was hard to transport significant quantities of goods by land. In particular, ships were crucial to transport of grain from Egypt to Rome and the distribution of grain ("bread and circuses") was necessary to prevent the Roman mobs from rioting.
The Mediterranean Sea was important to the expansion of the Roman Empire because of the fact that it was one of the main trade links used between all the different continents and regions of the Roman Empire. It was also much moe quicker to travel by boat than by road. The Mediterranean was also used to transport the food of Rome from Egypt, also known as the Corn Dole. Without the Corn Dole the mobs in Rome would have rioted.