Literary Device: Allusion

1548, from L. allusionem (nom. allusio) "a playing with, a reference to," from allus-, stem of alludere (see allude). An allusion is never an outright or explicit mention of the person or thing the speaker seems to have in mind. - Online Etymology Dictionary

Example:

No! I am not Prince Hamlet, nor was meant to be;
Am an attendant lord, one that will do
To swell a progress, start a scene or two,
Advise the prince; do doubt, an easy tool,
Deferential, glad to be of use,
Politic, cautious, and meticulous;
Full of high sentence, but a bit obtuse;
At times, indeed, almost ridiculous--
Almost, at times, the Fool.

Function:

In "The Love Song of J. Alfred Prufrock", Prufrock wishes to approach a woman and declare his love for her, but fears being rejected or disturbing the society around him. Seen in the lines above is a reference to William Shakespeare's "Hamlet". Prince Hamlet was an intellectual, passionate character who suffered from internal struggle and who took extreme, hasty action in the end. Eliot employs this reference to show that Prufrock was not a man of action or youthful passion. The reference to 'the fool' Polonius, the father of Prince Hamlet's lover, is further create's the idea that Prufrock is an old man. Perhaps to old to for a passionate act of love.