In the play's dramatis personae (literally, a list of the "persons of the play"), we're told that Gonzalo is "an honest old counsellor of Naples." He's travelling with the King's party when he's shipwrecked with the other passengers on Prospero's island.
The thing to know about Gonzalo is that he's a really good guy with an optimistic outlook on life—kind of like Dory in Finding Nemo, but with a beard instead of fins. The first time we meet Gonzalo, he's trying to break up a nasty argument between the royals and the mariners on deck during the tempest. While everyone around him is bickering and worrying about drowning, Gonzalo keeps his cool and says he's sure "good Fate" has something other than drowning in store for everyone on board the ship (1.1.31-32).
We also know that, when Prospero was booted out of Italy and set adrift with his infant daughter, Gonzalo was the one who made sure Prospero had enough food and water to survive. Gonzalo didn't just make sure Prospero would have supplies to physically sustain him, he also made sure Prospero had fancy linens and books—the kinds of things that would keep a guy like Prospero comfortable:
By Providence divine.
Some food we had, and some fresh water, that
A noble Neapolitan, Gonzalo,
Out of his charity, being then appointed
Master of this design, did give us, with
Rich garments, linens, stuffs, and necessaries,
Which since have steaded much. So, of his
Knowing I loved my books, he furnished me
From mine own library with volumes that
I prize above my dukedom. (1.2.190-200)
After washing up on shore, Gonzalo is the one who reminds everybody else that they should be celebrating because they're alive: "Beseech you, sir, be merry. You have cause— / So have we all—of joy, for our escape / is much beyond our loss" (2.1.1-3). Gonzalo gives voice to the idea that, despite the (seeming) loss of the ship, the survivors can uncover something even greater. In fact, this seems to be one of the play's biggest messages. Check out what Gonzalo has to say at the play's end:
In one voyage
Did Claribel her husband find at Tunis,
And Ferdinand, her brother, found a wife
Where he himself was lost; Prospero his dukedom
In a poor isle; and all of us ourselves
When no man was his own. (5.1.249-254)
Literary critic Robert Langbaum writes that Gonzalo's speech sums up the philosophy of the genre of tragicomedy—that we lose in order to recover something greater, that we die in order to be reborn to a better life." In other words, violence and tragedy are "all part of a providential design."
Notice the way Prospero associates Gonzalo with "fate"? Earlier, we saw how Gonzalo believes that "fate" determined whether or not he and the rest of the party would drown during the storm. Here, Prospero directly associates Gonzalo with the workings of "Providence divine," as if Gonzalo is an agent of fate. This is a pretty big deal because, in the play, we get the sense that some force greater than even Prospero's magic is at work guiding the lives of each of the characters.
Gonzalo also makes a big utopian speech that literary critics like to compare to a passage from Montaigne's "Of Cannibals," a famous essay that Shakespeare totally cribbed when he wrote Gonzalo's lines. We talk about this more in "Symbols" so check it out if you want to know more.