The eye is symbolic of the poet's conscience, as explained in an excerpt from this article by Mark McVann:
The poet-sirrah is plagued by his glass eye, which symbolizes conscience, and not only his own: he is also plagued because conscience is so easily ignored by some people, principally, of course, by Thon Taddeo. But even the Poet’s sensitive conscience is a fickle one: hardly scrupulous himself--he cheats old Benjamin out of a blue-headed goat, filches wine from the abbey’s cellars, and steals the thon’s boots--he nevertheless agonizes in titanic fashion over his desire for wine, but when, exhausted from the struggle he finally gives in, he takes out his glass eye and pours the bottle over his head rather than down his throat: “The advantage of a removable conscience, you see” (223). The Poet, who abandons the abbey for parts unknown, leaves his glass eye on the upturned wineglass at the monks’ banquet given for Thon Taddeo, telling the eye to watch the thon carefully (206). “So he thinks I need it more than he does.” Dom Paulo shrugged. “He’s only the Poet-sirrah!” The scholar puffed a breath of amusement....Suddenly he laughed. “I rather like that. I think I know who does need it more than the Poet” (223).