This quote comes in Act V, Scene 2, after a duel has been arranged between Hamlet and Laertes – Hamlet tells Horatio that he is uneasy about the fight despite having confidence in his own skills, and Horatio responds that he could send word to delay the duel, saying that Hamlet was unwell. Hamlet protests, stating “Not a whit, we defy augury: there’s a special/providence in the fall of the sparrow.” He then goes on to state that what will come will come, if not now then later – there is no avoiding one’s fate.
Augury is fortune-telling – the reading of omens or fates through divination. Hamlet’s uneasiness is an augur – an omen that he should not go through with this duel (he does not know that Claudius has poisoned the tip of Laertes’s sword, nor that he has set aside a cup of poison for Hamlet should he need a drink during the fight). And yet Hamlet ignores this feeling. If he has been fated to die, there is no use in simply delaying the inevitable by heeding some omen – he would rather confront his doom. “The readiness is all,” he states – he is willing to face his own death, for after all, “since no man has aught of what he/leaves, what is’t to leave betimes?” In other words, what does it matter if a man dies sooner, rather than later, if he will reap no rewards either way?
And so with this fatalist philosophy, Hamlet ignores his own gut feelings and proceeds with the duel, knowing that it will not end well for him. He has no love of life, and finds no sense in delaying the inevitable. Thus, by defying the augury of his own ill feelings, he rises dutifully to meet the fate that has been assigned him.
Hamlet's defiance takes place in Act 5.2. He comes to the realization that forces beyond man's control determine fate. This is a key realization for Hamlet who is now prepared to take action because he believes that the consequences of it lie beyond his control. It is this that he puts his faith in when he agrees to the swordfight (Line 202 "Not a whit we defy augury. There's a special providence in the fall of a sparrow....").
Note also the link to the Player King's words in Act Three Scene 2: "Our wills and fates do so contrary run/ That our devices still are overthrown; Our thoughts are ours, their ends none of our own."