In general, the play splices together two very different language styles.
In the play, blank verse (unrhymed iambic pentameter) is reserved for the nobles and high matters of state. Not only do the nobles speak poetry, they also tend to use a lot of fancy schmancy metaphors and grave words that make the characters come across as authoritative. (Though, Shakespeare makes characters like Hotspur and Glendower sound really silly now and then.) Check out this example of how King Henry tells the rebels they're in deep dog doo for rising up and causing the king's troops to prepare for war:
[…] You have deceived our trust,
And made us doff our easy robes of peace,
To crush our old limbs in ungentle steel:
This is not well, my lord, this is not well. (5.1.2)
Wow. We got so caught up in Henry's insistence that going to war's as uncomfortable as changing out of a pair of comfy pajamas and into armor (which is also what soldiers literally must do), that we almost forgot that nobody in England's been wearing "easy robes of peace" for quite some time – Henry's entire reign thus far has been plagued with civil warfare that he helped create when he deposed and murdered King Richard II. Nevertheless, his speech is pretty striking and we're totally impressed by the image of the king's army donning "ungentle steel" in preparation for limb "crush[ing]" battle. It makes the whole enterprise sound lofty and important, don't you think?
On the other side of the spectrum, Henry IV Part 1 reserves prose (how you and I talk every day) for the low-brow scenes involving commoners and degenerates like Sir John Falstaff and Prince Hal. (When Hal's being wild anyway. He's a character who slips between prose and poetry quite easily and you can read more about him in "Characters.") For now, check out how Shakespeare writes lines for one of the "Carriers" (sorry, he doesn't get a real name) as the character complains about the shoddy accommodations at a roadside inn in London:
Why, they will allow us ne'er a Jordan, and then we
Leak in your chimney; and your chamber-lie breeds
Fleas like a loach. (2.1.3)
Translation: The roadside inn (sort of like a Super 8 motel) doesn't provide chamber pots, so the Carriers have to urinate in the chimney. Plus, there's a major flea problem. (This is why we love Shakespeare – he's always surprising us.)
If you're thinking that King Henry and the Carrier seem to speak two entirely different languages, you're totally right, and it's not just because one speaks in prose about the low subject matter of fleas and urine while the other speaks poetry about the elevated topic of war. Henry IV Part 1 is famous for the way Shakespeare handles the vast linguistic range that was to be found in England. His characters, like real Englishmen and women, occupy different social stations and also speak according to regional dialects. In fact, much of what the Carrier has to say in Act 2, Scene 1 is practically indecipherable (especially to modern readers) and literally sounds like a foreign language compared to the way the nobility speaks. Recall also that Lady Mortimer performs a song in Welsh (she doesn't speak English and her father, Glendower, translates everything she says). See what we mean when we say the play's got a broad linguistic range? Be sure to check out "Language and Communication" for more on this.