Verse and Prose
Shakespeare wrote this play with his fellow playwright, John Fletcher. Naturally, the style of two writers can be very different, but these two playwrights fused their writing in this play well enough that the language flows from scene to scene.
The language in Henry VIII, like in Shakespeare's other plays, is a mixture of poetry (verse) and prose (how we talk every day). Here, Shakespeare switches poetry and prose up to show us whether a character comes from a higher or a lower class.
Poetry
We bet you've always wanted to know what iambic pentameter is. Right?
Don't let the fancy name scare you: iambic pentameter is the most common meter in all of Shakespeare, and it's pretty simple once you've got the basics down.
An "iamb" is an unaccented syllable followed by an accented one, like this: ba-DUM. "Pentameter" refers to a rhythmic pattern (meter) that has five (penta-) feet (iambs here) per line. Did that sound like Greek to you? Here, we'll break it down. Iambic pentameter sounds just like five heartbeats: ba-DUM, ba-DUM, ba-DUM, ba-DUM, ba-DUM.
Let's try it out on these lines from Henry VIII:
Would I had NEVer TROD this ENGlish EARTH
Or FELT the FLATterIES that GROW upON it! (3.1.43-44)
That's some Grade-A iambic pentameter right there. Since these lines have no rhyme scheme ("earth" and "it" don't rhyme), we call it "unrhymed iambic pentameter," which is also known as "blank verse."
Now, how often do you speak in blank verse? Probably not that often. Nobody speaks that way—it sounds too formal. In Shakespeare, it's usually only the nobles who speak in verse—you know, to show how noble they are. The lines above come from Queen Katherine, so it makes sense that they are in blank verse. She's as high up on the social scale as it gets.
Prose
Now, characters who don't get to speak in verse just plain talk. Take the Porter's lines when he's trying to keep everyone out of the palace gates, for example:
Belong to th' gallows and be hanged, you rogue!
Is this a place to roar in?—Fetch me a dozen crab-tree
staves, and strong ones. These are but switches
to 'em.—I'll scratch your heads. You must be seeing
christenings? Do you look for ale and cakes here,
you rude rascals? (5.3.6-11)
See how there is no pattern to the lines? That's because this dude is just talking; there's no meter here. This is called prose. Since this guy is just a lowly porter (or gatekeeper), he talks just like any regular guy would.