The Gellar Field is a energy field that protects a space ship, oneself, and crew from getting a Class 10 Clusterfucking from Chaos while traveling in the Warp. Most likely named after the real life fake psychic Uri Gellar.
As everyone knows, the only way to get anywhere without taking fucking forever is to use the Warp. That is, unless you are the Eldar, in which case you can go much faster with Webways as long as you don't get lost (actually Webways are usually slower, trading speed for safety). Or you are the Tyranids and can use gravitational Star Trek bullshit. Or you are the Necrons and can screw the laws of physics seven ways till Sunday. Or you are the Tau who invent new and less-shitty-then-previous but still-shitty-non-Warp-limit-as-x-goes-to-the-speed-of-light drives like every 20-30 years (well, we say “invent” but the Eldar noted their “crippling lack of creativity” so more like they go Blood Raven on intellectual property...so, like Space China but small). So maybe not everyone knows. But everyone definitely knows that all sorts of fucked up shit lives in the Warp, whose ONLY goal is to fuck you up (both literally and metaphorically) in 57 (or more) different variations. The Gellar Field prevents this from happening, so the Servants of the Imperium can go to your planet and kill your Chaos-worshipping ass!
The Warp, Giant Space Cathedrals and You
Its been mentioned a few times in the fluff that while the Gellar field on Imperial ships most definitely has a mechanical component, the field is reinforced by all the giant statues and gold bling that the humans of the setting feel the need to shove on every square inch of the hull. It actually makes a kind of sense when you think about it: The warp is a realm governed not by boring old logic but rather the thoughts and feelings of everyone in real space. Since Imperial ships are already borderline worshipped by humans as the physical manifestation of humanity's might and manifest destiny to rule the stars, turning them into actual space borne cathedrals (I.E. places of worship) could have an effect similar to the old belief that demons can't enter holy ground. Typically, this works pretty well as the greatest threat to an Imperial ship whose Gellar Field fails is the Warp itself, not the daemons. Daemonic incursions aboard are rare but not rare enough and the crew often manages to fight off the invaders either until they reach their destination or until they can safely drop out of the Warp. This ability to hold their ground likely is solely due to their faith and the holy ground thing. Notice that Imperial ships during the Great Crusade who suffered a daemonic invasion were unheard of. As in, never heard from again. Because atheism is a bad idea against enemies dominated by belief.
The True Nature of Gellar Fields
Highlighting how grimdark the Imperium is (as well as the fact that humans grudgingly need psykers), Ashes of Prospero and Farsight: Crisis of Faith both mention that the Gellar field's primary component is generated by the dreams of a psyker kept in a perpetual coma. According to Aaron Dembski-Bowden the idea that Gellar fields being powered by comatose psykers always been of the in-house 40k lore at Games Workshop at least as far back as Andy Hoare's time (so likely 3rd ed or earlier), and has only been revealed to the audience relatively recently. He also adds that the psykers tapped to power the Gellar fields burn out rather quickly and have to be replaced fairly often. Although the idea of psykers being wired up as Matrix-style batteries and treated like promethium tanks sounds grimdark as all hell, actually thinking about the implications of this reveals a huge number of plot holes.
Perhaps the biggest issue with Gellar fields being powered by the dreams of comatose psykers is that Dark Age of Technology humanity invented Gellar field generators by M15 (as that's when humanity invented Warp travel and began using it frequently), before there were any psykers around to power them. At the time of the Gellar Field's invention, the only psykers around (aside from the Emperor) were the artificially-created Navigators. Psykers only began appearing in large numbers by M25, and part of the reason for the Age of Strife is that Dark Age of Technology humanity was unfamiliar with psykers and did not know how to handle them in the first place. In other words, humanity would have to have been using a device powered by captured psykers for ten thousand years before they knew what psykers even were.
Additionally, Gellar Fields being powered by comatose psykers creates logistical issues. If comatose psykers are required for Gellar fields, this means that every ship in the Imperium, all the ships in the Imperial Navy, every Space Marine Battle Barge, every merchant chartership and civilian vessel, and all the ships of renegades who don't outright serve Chaos, all throughout the galaxy, now requires disposable psyker batteries to be able to Warp travel at all. It was already a stretch to believe they all had a handful of navigators, even discounting the chartist ships. Psykers are rare enough that the Imperium has an an entire institution dedicated to rounding up psykers and sending them to Holy Terra where they can be used to power the important things that do require psykers as fuel (like the Golden Throne or Astronomican). How do all these ships, which are often in far-flung corners of the galaxy and (in the case of the Imperial Navy and Rogue Traders) leave Imperial space for months at a time, find enough psykers to power their Gellar field generators? This issue is magnified even further if the psykers powering the Gellar fields burn out regularly and have to be replaced.
Finally, why would the dreams of a comatose psyker of all things be what projects the bubble of realspace surrounding the starship, when dreams are one of the most illogical and unrealistic parts of the human psyche? This is something that 40k lore actually touches on when it talks about how unreliable the astropath system is because it relies on communicating messages through dreams. If anything, one would expect a Gellar field produced by the dreams of comatose psykers to project the acausal and chaotic world of dream logic onto the confines of the ship, which is... basically what unprotected Warp travel is anyway.
Let's Take an Example
The Orks are a fantastic test case of what happens when someone who doesn't use Gellar Fields travels through the Warp.
The Orks can use a similar device to a Gellar Field, that focuses the power of the WAAAGH! into an energy field to keep the Daemons and other warp monsters away. It involves jamming Really Big Teef onto the ship in an effort to frighten passing Warp-monsters. Hell yeah! Maybe its a kind of ferryman payment to Gork or Mork for safe passage. Maybe it just inspires the weirdboyz and they keep trouble away. Who's to say? But it apparently works somehow, and even if it didn't the Orks would just give the unlucky daemons that tried to board their ship a good stompin'. The Orks like both outcomes.
Many grassroots WAAAGH!s get underway by hitching a ride on a passing Space Hulk. These are convenient because they can enter and exit the Warp (saving on having to make a very complicated Warp Drive), have tons of cargo space (for all of the boyz to ride in), and frequently come equipped with friendly passengers such as Genestealers, Daemons, Chaos Cultists, or other some forgotten horror (for in-flight entertainment). This travel method, while common for Orks, would be utterly disastrous for any other race. Space Hulks have no guidance systems: they can spend decades in the Warp and come out right where (and when) they started, or spend a few days in the Warp and arrive hundreds of years in the past around a totally uninhabited planet. While all of this waiting around is happening, the totally unshielded Hulk is ripe for invasion from Daemons, who not only look at Realspace beings as a food source but are actively drawn to anything Real that happens to pass by. Brainsuckers, sanity-feeders, life-drainers, and eight-million copies of Radical Larry are on standby to slither into the Hulk and track down any Ork stupid enough to have hitched a ride in the first place. All of that would be bad enough, but because the Warp and Realspace don't mix well, Space Hulks are constantly in danger of doing things like phasing into themselves, having infinitely-looping corridors and generally getting all M.C. Escher.
It's lucky for the Orks that they don't care much. Any other race would be driven mad, slaughtered entirely, and/or be devastated to learn that they arrived decades too late (or hundreds of years too early) to stop the conflict they were sent to fight. Orks by contrast will readily fight anything and everything, including themselves (and terrifying horror-movie antagonists) as a general first response to unpleasant or unfamiliar circumstances. Due to their below-average intelligence they generally take eldritch horror with a puzzled chin-scratch and eventual dismissal (or assault and battery). Ork WAAAGH!s are also fairly independent of things like nations or strategic timelines, so "showing up too late" is almost always a non-issue. (In one instance the Orks in question showed up too early, catching their own WAAAGH! right before it left. Long story short, the Warboss killed his past self to get two of his favorite gun and the WAAAGH! stopped in its tracks) The above is not to say that Orks who hitch a ride on Space Hulks are perfectly fine. They aren't. Many would-be WAAAGH!s begin and end when the horde jumps aboard a Space Hulk, and it shows up on the other side of the galaxy with a few thousand new sets of Ork skeletons inside.
Now I realize that this is gonna need some dumbing down, think of the Gellar Field as ways to enter a party. The Imperial way is to sneak in without drawing attention and getting swamped by the crowd. The Ork way of doing things is to jump into the sea as loud and as annoying as possible, either annoying everything away or, much like a college Frat party, drawing in things either like-minded or things FAR worse. but then again these are Orks we're talking about, they probably think whatever jumps on to their boat is just some fighting practice until they reach wherever they seem to be going.
Going to Shit, Possibly Literally So
As of the opening of the Great Rift, Nurgle has devised an insidious new plague that has allowed him to bypass the shielding of the Gellar Fields. The
"Gellarpox" *BLAM* Engineer's Syndrome works by infecting the laborers who maintain the Gellar Field generators, and more importantly it spreads through the generator itself (luckily, said generator has to be malfunctioning, but even a single minor malfunction can cause it to be infected). The infected humans show no initial symptoms other than strange dreams, but are subtly compelled to sabotage their work so the Gellar Field begins to weaken. When the time is right, they mutate and the infected generator turns into a horrific mass of biomechanical infectious tissue that endlessly spawns mutants, abominations, and the occasional daemon, almost certainly dooming the voidship the generator was formerly a part of. Although, it seems to keep doing its job so if you can hold the line until entering realspace and then blast the thing, you have a chance.