The Hunmin Jeongeum Haerye, the treatise introducing the principles behind the Korean alphabet written by its inventor King Sejong in 1446, explains that this glyph was derived by adding a stroke to ㄴ (n, “n”), which itself is a visual representation of the tip of the tongue touching the upper palate (presumably of a person facing left), because both /n/ and /t/ are coronal sounds.
Gari Ledyard proposes that Sejong derived ㄷ from the 'Phags-pa letterꡊ(t), and that ㄴ was in fact created by removing a stroke from ㄷ. Ledyard gives evidence that Sejong was inspired by 'Phags-pa for the basic glyph forms, although he changed the shapes of the letters drastically in order to enhance the simplicity and rationality of his script, and the ultimate shape of the letters may indeed have been influenced by that of the speech organs (Ledyard 1997).