Elizabethan Drama evolved from the Miracle. Mystery, and Morality plays of the Middle Ages. Perhaps the most famous of these plays is Everyman.
The biggest step came with the so called "school dramas". The first tragedy was by two school friends, Thomas Sackville and Thomas Norton called Gorboduc. The first two comedies were Ralph Roister Doister by Nicklas Udal and Gammer Gurton's Needle, playwright unknown. These plays are all in verse which is rather awkward and clumsy.
It was left up to the University Wits (Lyly, Lodge, Greene, Nashe, and Marlowe) to further develop both the form and the verse. The most influential of this group was Christopher Marlowe who took blank verse which was already being experimented with by some of his peers and used it better and more eloquently.
Quit simply, blank verse aka iambic pentameter is a rhythm, de DUM de DUM de DUM de DUM de DUM. It was used for several very practical reasons. Earlier verse forms were clumsy whereas blank verse most closely mirrors the rhythm of everyday English speech. (IE I asked for coffee but you gave tea.) It also mirrors the heart beat and finally verse is easier to memorize than prose because of the rhythm. (It is interesting to note that the rhythm is called iambic pentameter. In Greek iam means to throw, meaning the verse is always being thrown forward.)
Marlowe also used the closet dramas of Seneca as his model rather than the more rigid Greek. Both Marlowe and Thomas Kyd (The Spanish Tragedy) brought the violence right onto the stage to the delight of the Elizabethan audiences. In Elizabethan tragedies, the bodies pile up on stage.
Unfortunately, Marlowe died young in a bar room brawl or who knows what he would have accomplished as a playwright? Fortunately, William Shakespeare was there to pick up the mantel of "master of the verse". Shakespeare continued the development of blank verse and used it effectively in all of his plays.
He also used prose. Often prose is the language of the lower class but not always. It can also be used among friends. For example King Lear opens with two nobleman "having a chat". They are speaking in prose. When the king enters and the occasion turns formal, so does their language. They speak verse.
The play, Much Ado About Nothing is more than half prose whereas in Romeo and Juliet, Mercutio speaks in prose but few other characters do. Here Shakespeare used a lot of rhyming couplets which is an indication of wrapping up an idea/thought.
Shakespeare can give you a good picture of a character's state of mind by how he uses verse. If the language is smooth and flowing, this is a mentally calm and in control character. If the language is short and choppy with lots of punctuation, the mind is in turmoil.
Shakespeare seemed to choose the language, whether it was verse, prose, or a combination of the two for each character according to need and situation. Not every line is in the 5 stress/5 unstressed pattern. Sometimes the rhythm is a troke. Key words are always in the stress position. It must be remembered that seemingly unimportant words like if or and can be in the stress position.