Howdy there! Cid's the name. I'm from Canaan, but I've been stuck here ever since Nelv Valley got blocked by a giant rock.
Cid Haze is an airship mechanic. He was visiting Inner Sasune when the great earthquake happened, causing a giant rock to fall on Nelv Valley. On top of that, the Djinn was released and cursed everyone in Castle Sasune and Kazus to become ghosts, Cid included. Luckily, four youths from Ur happened to be passing through. Confident in the kids' ability to save them, Cid tells them where he parked his airship. His trust proves warrented as the youths defeat the Djinn and return everyone back to normal.
Joining with the youths, Cid works with the local blacksmith, Taka, to create a battering ram to destroy the boulder blocking Nelv Valley. The ram works at the cost of Cid's airship, but the old man takes it in stride. He returns to Canaan only to discover his beloved wife had grown ill in his absence. Luckily, the Onion Knights were also in Canaan and generously give Mrs. Cid an Elixer they found. Grateful, Cid gave the kids his stash of items in the airship hanger. Later the kids approach Cid with the Wheel of Time, a device that is used in Airship construction. Cid installs it into their boat, turning it into an airship.
Cid is the second in a proud tradition for the series: Much like Sara, the Cid is usually used for an airship engineer. Unlike Sara, Cid is a much more consistent presence, appearing in almost every game (FF1 being the exception and even that was eventually grandfather'd in) as well as being a significant presence in spinoffs. In a Final Fantasy game, there will almost always be a Cid and he will usually (albeit, not always in spinoffs) be linked with an airship of some sort.
Cid Haze is a jolly old man, a contrast with FF2's Cid who appears younger and is more of a gruff fellow. He carries on the soon-to-be tradition of being an airship specialist; owning an airship at the beginning of the game and helping the party upgrade the Enterprise into one later. Not much of Cid's past is really noted, but he's friends with Taka the blacksmith and he notes that he used to work for King Argus.
If there is one guest who was so fundamentally changed by the remake, it was Cid.
Early on, Cid has a similar role to the Famicom game. However, there are a few moments where Cid hints that he's more familiar with the protagonists than he lets on, though he refuses to elaborate for the most part. It's only after the four come to him with the Wheel of Time that he finally explains the truth: Cid and the Warriors of the Light are not native to the floating continent.
10+ Years ago, Cid used his airship to ferry people around. When the Flood of Darkness hit, he wound up crashing onto the Floating Continent. In the end, the ones who survived were himself and four kids who would grow up to be chosen by the crystal. He concludes by saying that he doesn't know what happened to their world after the darkness hit, but if anyone could figure it out, it's the Warriors of Light.
While the game doesn't directly touch on this plot point again, dialogue in Saronia suggests that Cid was originally from there; Speaking with the scholars around the castle has them note that there was once a genius inventor who resurrected the Nautilus and vanished when the world became covered in darkness. It should be noted that the english localization messes up this section due to a misinterpretation: The translator was seemingly unaware that the "Ancient Ruin" that the scholars describe was an actual area, and thus the inventor is described of being of "Saronia of Old" and that he invented the Nautilus.
During battle, Cid either uses the Fira spell or attacks physically with a hammer.
While Cid is not directly tied to any of the four in particular, he interacts the most with Luneth and mentions Luneth specifically when Doga summons him to help the Warriors of Light during the climax.
Surprisingly, there is little to no unused content for Cid Haze.