What is the literary device "diction"? Cite a example in Hamlet.

Diction is not simply word choice.  It is a total package of the author's language that conveys mood, attitude, style, and dialect.

So says Bedford St. Martins:

A writer’s choice of words, phrases, sentence structures, and figurative language, which combine to help create meaning. Formal diction consists of a dignified, impersonal, and elevated use of language; it follows the rules of syntax exactly and is often characterized by complex words and lofty tone. Middle diction maintains correct language usage, but is less elevated than formal diction; it reflects the way most educated people speak. Informal diction represents the plain language of everyday use, and often includes idiomatic expressions, slang, contractions, and many simple, common words. Poetic diction refers to the way poets sometimes employ an elevated diction that deviates significantly from the common speech and writing of their time, choosing words for their supposedly inherent poetic qualities. Since the eighteenth century, however, poets have been incorporating all kinds of diction in their work and so there is no longer an automatic distinction between the language of a poet and the language of everyday speech.

Examine the famous soliloquy from the Prince:

To be, or not to be: that is the question:
Whether 'tis nobler in the mind to suffer
The slings and arrows of outrageous fortune,
Or to take arms against a sea of troubles,
And by opposing end them? To die: to sleep;
No more; and by a sleep to say we end
The heart-ache and the thousand natural shocks
That flesh is heir to, 'tis a consummation
Devoutly to be wish'd.

Shakespeare's diction is very formal and fraught with imagery, metaphor, poetic devices, rhetorical questions, and philosophy.  We can tell that the speaker is using elevated language (poetry) in perfect iambic pentameter to deliver a soliloquy that comments on his emotional state and the action of the play.

Through his diction, we can tell that Hamlet is very intelligent and introspective, even suicidal.  He is questioning whether to exist the way he is or to put up a fight against his own feelings and enemies.  His dialect is not realistic; Danes or Elizabethans didn't speak this way.

Rather, his diction is used for dramatic effect.  It is meant to be heard.  It calls attention to itself.  It is intentionally vague: "to be or not to be."  And yet very complex: it has multiple meanings.