What is universally thematic about the scene is its depiction of suffering. There are many aspects to that theme, of course. If we are to be more specific, the miscommunication, anger, and antagonism that are expressed by Hamlet are illustrative of the incompleteness, the insufficiency that comes of a failed relationship—but also of the failed life he believes he has led.
It's clear that Hamlet is through with Ophelia. Whether she is really through with him is open to question. She is basically following her father's and brother's orders to avoid Hamlet, and she thus attempts to return his gifts. But when he coldly answers, "I never gave you aught," her responses indicate she's probably still in love with him.
The rant that follows from Hamlet is evidence at least of the abusiveness that is a part of his personality. But in most interpretations of the play, the root of this is Hamlet's inner torment. He is disgusted with the whole situation at court, in which he's aware his father has been murdered and the murderer has married Hamlet's mother. He's disgusted with himself as well. Hamlet's character is one of self-disappointment and self-loathing, and he takes it out on Ophelia.
Whether Hamlet is shamming madness in this scene or has genuinely gone crazy, there is no way of knowing. Whichever it is, the man's suffering has such an intensity he cannot control it. We also have no final answer to how much of this is due to either his belief that Ophelia is rejecting him or his wish simply to dump Ophelia. Or, it may be that the idea of sexuality in general has become revolting to Hamlet, and he takes it out on her with his injunction "Get thee to a nunnery!" His disgust with life is so great that he wishes humanity to stop reproducing: "I say we will have no more marriage." He also gets in his cuts against Ophelia's father.
This last point, like everything else in Hamlet, is open to wide interpretation. Arguably it's not just Polonius he is referring to:
Let the doors be shut upon him, that he may play the fool nowhere but in 's own house.
Hamlet has come to believe all men are playing the fool, not just the clownish (in most interpretations) Polonius. He has become anti-life, as if the usual associations among people should somehow be negated. And yet, as we have just heard from him, he has not the courage to take his own life, fearing "the undiscovered country, from whose bourn no traveler returns."