Upon the inception of the United States of America -- America had no real navy of any import, and therefore was at the mercy of maritime powers such as the United Kingdom when it came to international waters. In fact, the resolution of the American Revolution would probably been markedly different, had it not been for the power and timing of the French fleet that aided the American cause. In any event, in any era in which flight by air was unknown and inconceivable; meant that trade between nations that were separated by vast bodies of water was conducted through ships of the sea. This thus meant that a priority of America was to develop not only ships of trade but also ships of war to therefore protect their interests.
Additionally, ships of yesteryear were quite obviously not powered by anything other than wind, which meant that ships were susceptible to being attacked or taken over by other ships that were faster or well placed to do so. Further, within a very short distance off of the coast of Florida, lies the Caribbean islands, of which, those islands were claimed by various European powers and further to the point, the sea lying off of these islands was considered to be the territory of those islands and hence controlled by those foreign powers; in which, any ships sailing too closely to the shore of those islands or within the bounds of the territory so claimed by those islands, was considered to have ventured into foreign waters.
So then, the fact that within a very short distance from America, were islands that were under European control, meant that the United States was in danger of possibly being attacked from those ships massing upon those islands in order to contemplate doing so. In addition to the fact that ships so stationed there could easily be supplied and retrofitted; America also had to contend with the fact that their own ships, rightly or wrong, could be considered to have violated foreign waters, which may in and of itself, initiate some sort of retribution or even war.
This so signified to America, that at some point, it would be important to that country's sovereignty, to thereby take control of by the purchase of, or the winning of in war, at least one of the main islands in the Caribbean; of which that island would need to be large enough to handle ship traffic, as well as having a good and safe port. Ultimately, that indeed did happen, with Puerto Rico becoming an American territory, along with the United States Virgin Islands. This meant that within the Caribbean, that not only did the United States now have the ability to have its own naval base, but also that within the Caribbean, the United States would no longer be at the mercy of those other nations, claiming that their territorial waters had been violated; for the United States would now be able to claim such waters as their own, and because of America's proximity to the Caribbean, be in a far stronger position to enforce such.
The seas of this world are still absolutely vital, for maritime traffic is still the way that a significant amount of international trade is conducted, of which, it is of vital importance to any nation, that the waters that they travel upon, be open and international in scope, or under their control, so that they subsequently need not ever travel wittingly within foreign waters.