The Great Sea makes up the deep waters between the continents of Azeroth. It surrounds the Maelstrom. Every single sea in the world connects to it. This stretch of sea is so vast you will die of fatigue before you can swim any significant distance. In order to cross it, the Horde primarily uses zeppelins and the Alliance uses boats.
The Great Sea did not exist prior to the Great Sundering. After the Well of Eternity was destroyed and Kalimdor was split asunder, the waters that filled in the void became known as the Great Sea.
When the Horde ravaged the Kingdom of Azeroth and killed its advocate, King Llane, Anduin Lothar rallied his countrymen and charted their retreat across the Great Sea — and onto the shores of Lordaeron.
Since the War against the Lich King, the Great Sea has become more heavily traveled by both Horde and Alliance. The two have had numerous naval skirmishes.
The Cataclysm caused many changes in the Great Sea, and several new locations became accessible to players: The goblin isle of Kezan and the Lost Isles are located just southwest of The Maelstrom, but are unreachable except during the goblin starting questlines. The Maelstrom itself, damaged by Deathwing, has opened a portal directly to the Elemental Plane of Earth, Deepholm, reachable only to those specially summoned there. The reef of Vashj'ir off the coast of the Eastern Kingdoms became accessible, and the Horde and Alliance are recruiting seasoned soldiers to explore and claim the territory. Off the coast of Gilneas, the island kingdom of Tol Barad is another point of contention between the Horde and Alliance, who are constantly fighting for control. In an unspecified location on the Great Sea is Darkmoon Island, which hosts the mysterious and slightly sinister Darkmoon Faire on the first week of every month.
Other locations on the Great Sea, such as the Undermine and the Broken Isles, are largely unexplored, but may await travelers in the future.