The full "silent interview" is here, in Act 2, scene 1:
My lord, as I was sewing in my closet,
Lord Hamlet, with his doublet all unbraced,
No hat upon his head, his stockings fouled,
Ungartered, and down-gyved to his ankle;(90)
Pale as his shirt, his knees knocking each other,
And with a look so piteous in purport
As if he had been loosed out of hell
To speak of horrors, he comes before me...
He took me by the wrist and held me hard;
Then goes he to the length of all his arm,
And, with his other hand thus o'er his brow,
He falls to such perusal of my face
As he would draw it. Long stay'd he so.
At last, a little shaking of mine arm,
And thrice his head thus waving up and down,
He raised a sigh so piteous and profound
As it did seem to shatter all his bulk
And end his being. That done, he lets me go,
And with his head over his shoulder turn'd
He seem'd to find his way without his eyes;
For out o' doors he went without their help,
And to the last bended their light on me.
I have always viewed this seen as the first part of Hamlet's elaborate plan to "catch the conscience of the King." He is play acting. Remember, at the end of the previous act, Hamlet, after seeing and speaking to the Ghost, warns Horatio and Marcellus to swear secrecy and tells them this:
Here, as before, never, so help you mercy,
How strange or odd soe'er I bear myself—
As I perchance hereafter shall think meet
To put an antic disposition on—
That you, at such times seeing me, never shall,
With arms encumber'd thus, or this head-shake,
Or by pronouncing of some doubtful phrase,
As “Well, well, we know,” or “We could, an if we would,”
Or “If we list to speak” or “There be, an if they might,”
Or such ambiguous giving out, to note
That you know aught of me; this is not to do,
So grace and mercy at your most need help you,
In short, he tells them that he may act a bit nuts at times. Thus, Hamlet goes first to his girlfriend Ophelia. She is the daughter of gabby busybody Polonious, adviser to King Claudius. He knows such strange behavior will be communicated from daughter to father and then to Claudius. Hamlet wants Claudius to be nervous, on edge, aware of the young, dark prince, and bothered by him. And he gets just what he wants.
One may not agree that this is the best way to go about taking one's revenge on a remorseless villain, but it is Hamlet's way.
This is a turning point for Hamlet. Whenever a Shakespearean character, especially the tragic hero, doesn't speak, it is significant. Whenever a tragic hero moves from language to silence or language to action, it is that he cannot trust words any more. What speaks more about a person, their words or actions? Regarding Ophelia's, Hamlet may have said the former, but now that he is on his mission of revenge, he has uncovered the latter. He knows he cannot trust words, love, marriage, women. He is resolving himself to become a man of action.
Why doesn't he speak to Ophelia? Does he believe this will be the last time he sees her? Has he not been so deceived by words and her that he now trusts neither? Doesn't he know that Ophelia is now in league with his enemies (Polonius and Claudius)? Doesn't he know that Ophelia wants this interview, to gain information from him that she will later relay to Hamlet's enemies?
Words, words, words...no more.