I've never really seen it explicated, but it contains a few mysteries for me.
High and mighty,
You shall know I am set naked on your kingdom. Tomorrow shall I beg leave to see your kingly eyes, when I shall, first asking your pardon thereunto, recount the occasion of my sudden and more strange return.
"High and mighty" sounds sarcastic, but Hamlet does seem to be making a point that he's coming alone and unarmed, unlike, say Laertes who comes with a mob at his back. However, "your kingly eyes" can't be anything but mockery. It's the sort of thing Osric would say with a straight face. The language is slyly pompous. "When I shall, first asking your pardon thereunto . . ." And then the purpose: I wish to tell you just how the hell I got back here. Should be interesting for you.
I see this as Hamlet's getting ahead of events in his inimitable fashion. He's not going to sneak back into Denmark and hide somewhere only to be found out by spies or informants -- no, he's going to attack first by announcing his return right to Claudius himself. Moreover, he does so with his eternally sly, biting, and mocking humor.
And to what reception? Why, Claudius and Laertes just can't make it out! At least they have the sense to see that if this guy's going to be stopped, it better be soon and it better be certain.
But here's my big question: I would love to know just what Hamlet would have said if he had shown up in court on his own, without Claudius's invitation to the duel.