Henry VI, Part 3 is kind of an anomaly for Shakespeare. Most of his plays are written in a combination of verse (poetry) and prose (how we talk every day). The nobility tend to speak in "blank verse," which is a formal way to talk. The commoners or "everyday Joes" tend to speak just like we do, in regular prose.
But—possibly because it doesn't really have many common folk—this play is written entirely in verse. That's right: from the lowly soldier all the way up to King Henry, everybody speaks in verse. Some scholars disagree with this and say that some lines in the play are a bit long or complicated to be what we know as verse and so are probably prose. But for the most part, people will tell you that this play is entirely verse, specifically iambic pentameter.
So what is iambic pentameter? Don't let the fancy name intimidate you; iambic pentameter is pretty simple once you get the hang of it.
An "iamb" is an unaccented syllable followed by an accented one (one of those pairs is called a "foot"). "Penta" means "five," and "meter" refers to a regular rhythmic pattern. So "iambic pentameter" is a kind of rhythmic pattern that consists of five iambs (or feet) per line. It's the most common rhythm in English poetry, and it sounds like five heartbeats: ba-DUM, ba-DUM, ba-DUM, ba-DUM, ba-DUM.
Let's try it out on this line, where King Henry VI prophesizes that little Henry of Richmond will become king one day:
His LOOKS are FULL of PEACEful MAjestY,
His HEAD by NAture FRAMED to WEAR a CROWN
Every second syllable is accented (stressed), and there are five "feet" in the line, so this is classic iambic pentameter. Since the lines have no regular rhyme scheme ("majesty" and "crown" don't rhyme), we call this unrhymed iambic pentameter, or blank verse.