Grab those sunglasses, because we're about to look at the sun. When Buckingham first tells us, "I wonder / that such a keech can with his very bulk / take up the rays o' th' beneficial sun / and keep it from the Earth" (1.1.63-66), we'll admit we're a little confused. After all, how do you steal the sun?
Well, we soon figure out that the sun represents the king. Shakespeare does this in a lot of plays: he uses the sun to symbolize the monarch because of its power, brightness, and strength. Take a look at what Wolsey says about this when he's talking to Cromwell, "Seek the King; / that sun, I pray, may never set!" (3.2.493-494). Sadly, Wolsey does set (turns out he's not the sun), as do a lot of other characters. But the sun—Henry—is everlasting, and keeps on shining, even when the play is up.
On top of that, though, the fact that Henry is associated with the sun clues us in to the fact that everything in this play is happening because of him. Because he's got absolute power, all the power-hungry characters in this play have to learn how to manipulate him to get what they want—that's why there's so much intrigue and so much back-stabbing.
That's also why there's so much death and suffering: the only way to get more power for yourself is to make the king himself get rid of the people in your way. How do you do that? Well, one thing you can do is charge them with treason. It's pretty much impossible to prove that you haven't committed treason, and the punishment for it, conveniently, is death. That sure gets people out of the way in a hurry.
Get too close to the sun, and you might just get burned.