The Hidden Half is the name given to all the parts of Arda below the edge of the world, where all that existed were the Martalmar, the foundations of the earth, as well as the lowermost regions of the Encircling Seas and the airs of Ilmen. The Mountains of the West and East prevented anyone from finding the Hidden Half of the world.
Vaiya, that flows completely around the world, forms a sea below it, and it seems like the world "floats" on that sea. Ulmo the Lord of Waters dwells in Vaiya, below the Martalmar.
 See also
J.R.R. Tolkien, Christopher Tolkien (ed.), The Shaping of Middle-earth, "V. The Ambarkanta" pp. 242 - 243
J.R.R. Tolkien, Christopher Tolkien (ed.), The Shaping of Middle-earth, "V. The Ambarkanta: Of the Fashion of the World"