The U.S. Navy has found its place in defending the Internet; underwater. That's where most of the planets Internet traffic spends most of its time, as it travels from continent to continent via fiber-optic cables. The navy proposes to undertake more aggressive operations to prevent terrorists, or hostile nations, from trying to cut these cables.
American submariners need all the work they can get, especially since they are fighting hard to get money to replace their rapidly ageing boats. Its an uphill fight. Submarines havent been used much in combat for over sixty years. That means they have not had a chance to prove how useful submarines can be.
Four years ago, the navy began admitting to missions that were long known, but not admitted. There were the Cold War missions to tap into Russian undersea communications cables. For all we know, American subs are still doing this. It's not the sort of thing you admit to.
The U.S. navy has built up a lot of experience, and specialized (and often still secret) equipment for these missions. What the navy now proposes is to use some of this knowledge to help guard these fiber-optic cable networks. The navy has a lot of specialized equipment for this. In addition to the "spy submarines" (including the Jimmy Carter, a Seawolf class boat built specifically for these missions), there was (and still is, to a certain extent) the undersea passive sonar system. During the Cold War, there were several networks of these underwater listening devices, which could detect ships and subs over a thousand kilometers away. The U.S. still maintains a lead in that kind of technology, as well as other techniques for tracking underwater traffic.
While it's possible for a hostile party to cut underwater data cables, it's even more likely to happen by accident. There have been several cables cut by ship anchors in the last few years. It's very easy for this to happen. Then there are natural disasters (undersea landslides and earthquakes). While the navy can't do much about accidents, they do (in cooperation with the U.S. Coast Guard) keep track of a lot of the merchant and military ships on the world's oceans. If the navy has a plan for Internet defense at sea, much of it will involve black (secret) projects. So you won't hear much about it until it's all over.