King Lear, like Shakespeare's other plays, is written in a combination of verse (poetry) and prose (how we talk every day). (Note: The play Richard II is the one exception to this rule – it's the only Shakespeare play written entirely in verse.)
Reading King Lear often feels like reading a very lengthy poem and that's because Shakespeare's characters often speak in verse.
What kind of verse do they speak? Well, the nobles typically speak in unrhymed "iambic pentameter" (also called "blank verse"). Don't let the fancy names intimidate you – it's pretty simple once you get the hang of it. Let's start with a definition of "Iambic Pentameter":
An "iamb" is an unaccented syllable followed by an accented one. "Penta" means "five," and "meter" refers to a regular rhythmic pattern. So "iambic pentameter" is a kind of rhythmic pattern that consist of five iambs per line. It's the most common rhythm in English poetry and sounds like five heartbeats: ba-DUM, ba-DUM, ba-DUM, ba-DUM, ba-DUM.
Let's try it out on this line from King Lear:
since NOW we WILL diVEST us BOTH of RULE
Every second syllable is accented, so this is classic iambic pentameter. When the lines have no rhyme scheme, we call it "Unrhymed Iambic Pentameter," which is also known as "Blank Verse."
Blank verse, as we've said, is typically reserved for the nobility and other important characters since it's kind of a formal way to speak. In the first half of the play, King Lear speaks almost entirely in blank verse, which is befitting of his social station.
Not everyone in the play speaks in blank verse, which we've established is an elegant, high-class way of talking. In Shakespeare's play's, characters lower on the social scale don't talk in a special poetic rhythm; they just talk.
In King Lear, it's worth noting that that prose speech is often a sign of madness. When Lear goes insane, he often rants in prose and then switches back to eloquent blank verse, which alerts the audience to the fact that Lear is losing his mind. (Psst. You might want to compare Lear's prose rants to what happens to Ophelia in Hamlet. When Ophelia goes mad, she speaks prose and also communicates through song.)