Most of this play is written in verse (poetry) and the rest in prose (the way we speak normally).
We break all of this down in the paragraphs that follow, but here's one thing to remember about Shakespeare's plays: generally speaking, the nobility (like Antonio, Portia, and Bassanio) tend to speak in blank verse, which is a pretty formal way to talk. The commoners, or "everyday Joes" (like Gobbo and Lancelot), tend to speak like we do, in regular old prose. (Note: The play Richard II is the one exception to this rule – it's the only Shakespeare play written entirely in verse. Even the gardeners speak poetry.)
Here are some specific examples from The Merchant of Venice.
Like we said, the noble characters mostly speak in unrhymed iambic pentameter (also called "blank verse"). Don't let the fancy names intimidate you – it's really 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:
da DUM, da DUM, da DUM, da DUM, da DUM.
Check out the play's opening lines, where our mopey merchant of Venice (that would be Antonio) tells us he's bummed out:
in SOOTH, i KNOW not WHY i AM so SAD
it WEARies ME; you SAY it WEARies YOU (1.2.1)
Every second syllable is accented (stressed), so this is classic iambic pentameter. Since the lines have no regular rhyme scheme, we call it unrhymed iambic pentameter, a.k.a. blank verse.
Not everyone in the play speaks in verse. Ordinary folks, as we've said, don't speak in any special rhythm – they just talk. Here's an example where Antonio's servant delivers a message in plain old prose:
Gentlemen, my master Antonio is at his house and
desires to speak with you both. (3.1.1)