"The Waste Land" is written in such a way that the scattered scenes and quotations appear to be fragments left over after the total devastation of World War I. The words "Those are pearls that were his eyes" are apparently what some unidentified person remembers from reading Shakespeare. All that the stunned person quoting the line apparently has retained in his or her memory is that one line. Everything else may have been lost to humanity. Only scraps are retained by isolated individuals. The line in question comes from a little ditty sung by the spirit named Ariel in The Tempest. Ariel is spreading misinformation to the survivors of the ship supposedly sunk by the tempest raised by Prospero, making them all believe they are the only survivors. Ariel's entire song is as follows:

Full fathom five thy father lies.
Of his bones are coral made;
Those are pearls that were his eyes;
Nothing of him that doth fade
But doth suffer a sea-change
Into something rich and strange.
Sea-nymphs hourly ring his knell:
Hark, now I hear them,—Ding-dong bell.
Act 1, Scene 2

There appears to be a relation between the reference to Ariel's song in "The Waste Land" and a later description of the death of Phlebas the Phoenician in Section IV: Death by Water in Eliot's famous but often cryptic poem.