(covers information from several alternate timelines)
Utopia Planitia was a vast lava plain on the planet Mars. It hosted the surface structures of a starship construction facility, the Utopia Planitia Fleet Yards, one of the Federation's most extensive construction yards.
Benjamin Sisko was stationed on Utopia Planitia between the death of his wife (at Wolf 359) and his posting on Deep Space 9. (DS9: "Emissary") While on Utopia Planitia, Sisko worked on the prototype USS Defiant – the first in what was to be a fleet of warships to defend the Federation from the Borg. After work on the project slowed, and design flaws became apparent, the project was shelved. (DS9: "The Search, Part I", "Defiant")
According to the Star Trek Encyclopedia (3rd ed., p. 538), the plain was "first explored by the automated space probe Viking 2, which softlanded there on September 3, 1976, part of Earth's first attempt to employ spaceflight in the search for extraterrestrial life."
"The city of Utopia Planitia in 'Lifesigns' was a matte painting by Dan Curry, based on designs by Anthony Fredrickson and Doug Drexler. The fact that the Enterprise-D was supposed to have been built at Utopia Planitia was inscribed on the dedication plaque for the ship located on the main bridge. A copy of the dedication plaque was included in a CD-ROM collection of art and literature assembled by the Planetary Society and was launched toward the surface of Mars aboard the Russian Mars 96 space probe, although the probe never made it out of Earth orbit due to a launch vehicle malfunction."
The painting of the surface facilities in "Parallels" was by Rick Sternbach and Michael Okuda. (Star Trek Encyclopedia (2nd ed., p. 21)) Asked if construction indeed was intended to take place on the surface of Mars, Okuda answered:
"Yes, that was the intent, although I like the suggestion that it might have been a training facility. It was something that Rick and I put together in Photoshop. I don't recall exactly who did what, but I remember that the upper image uses a bunch of simple paper models that we made for use as [...] generic futuristic city buildings for exactly this sort of image. Rick may remember more about this. I do recall that we wondered how the components would be brought into orbit, whether they'd be beamed up, hauled up by space elevator, or carried by a huge orbital tug [....] "It [surface construction] certainly would be difficult, and I personally think that it would be more likely that the major component assembly would be done in orbit. I believe that Rick felt this way, too. Still, impulse engines routinely accelerate starship masses (many tens, even hundreds of thousands of tons) to large fractions of the speed of light in very brief times. This suggests a propulsion technology many thousands of times more powerful than anything we have in the 21st century. Also, structural integrity fields would need to protect against these accelerations, which conservatively would exceed 1,000 gees. As a result, I'd contend that lifting major starship components into orbit from the surface of Mars would be well within the reach of Star Trek's postulated technology."
In Sternbach's explanation of the painting, he suggested it to be a "systems integration simulator," adding, "the hardware seen on the surface could be the real vessel parts, which were probably only 20% filled with "stuff" and then lifted into orbit for final assembly. If not, then they are flight-quality hardware used as a functioning lab to make sure everything works as designed."