FTL travel

FTL, the ability to travel faster than light, and specifically the drive. Essentially a refined Alcubierre warp drive, it uses negative/exotic matter (shut up, i don't know nearly everything about it, and the topic gets very complex, fast, close enough.) to warp spacetime ahead and behind it to effectively go thousands of times the speed of light. Consumes FTL fuel, which can only be made effectively in certain areas and locations, but is decently common.
Most warp drives are on a scale, by number. From 1 to, well wherever. The highest thus far are used on interstellar tradeships, the ones that range to over 50km long, having a class-58 at highest. These classes scale for the size of the ship, so the larger the ship, the higher the class. This does not mean you need a specific class for a specific ship, as the class determines the distance relative to mass. The Star-Reaver, for example, has a class 15 drive. This is overkill for that size a ship, but allows it to travel hundreds of thousands of lightyears without refuel. Most of the classes of drive below 10 are very uncommon nowadays.
There's also Causal Correction, a phenomenon unique to FTL travel, which poses a risk towards careless use of FTL drives. This also largely eliminates the need of large-scale reinforcement against larger particles in space, as their immense relative speed to the ship will nearly certainly cause them to vanish.

Skejon: "So, what's wrong with it?"
Jon: "You want a proper, thorough explanation?"
Skejon: "Sure."
Jon: Sighs. "The mechanism that keeps the negative matter in its container is nonfunctional, and the electromagnet controlling passage to the drive itself is being constantly powered. Also, the main drive is in continous projection mode, and trying to turn it off improperly would result in the isolated space of non-warped spacetime collapsing on the ship. That would cause the warping of spacetime to travel across the ship, tearing it apart on the quantum level. On top of that, such a rapid and asymmetrical shift from superluminal travel to subluminal would end up in causing all sorts of unpredictable causal violations, and thus also invoking causal correction, which would at best do nothing and at worst erase all of us from reality. Even if we survive that, we'll still be stranded in space far from the nearest human system with limited fuel."
Skejon: "I understood around half of that, that's not good, right?"
Quaken: "I have no clue."
Jon: "The drive is stuck on and if I don't turn it off carefully we will certainly die, at best."

Utility

Travel between massive distances in space. Before FTL, ships had to go to other systems on multi-decade voyages. The fastest ships out there, with antimatter engines, could accelerate to around 0.7c, 70% the speed of light. Fast, but still slow for interstellar travel.

Manufacturing

The manufacture of FTL engines is not easy by any means, but a large factory can produce them in good capacity. The fuel, too, is somewhat difficult. Large amounts of energy are needed, and it can only be produced in dedicated refineries, usually powered by antimatter reactors.

Social Impact

Absolutely revolutionary. When before poeple had to fall out of society for decades at a time, and either A. spend decades, maybe even a century or more aboard the same ship, with the same people, or B. Be essentially dead in cryosleep, now people can be from point A to point B, even a hundred lightyears apart, in a day or so. This has also hastened wars and conflicts, as well as allowed for more unified interstellar nations.

Access & Availability

Very accessible, even usable on personal civilian craft. Not dirt cheap though, and on planets like Ochtotne Prime, only a handful of ships have drives, tradeships and heavy cruisers, totalling less than 10.

Complexity

Very. Manipulating spacetime ain't easy. This is what the math looks like.

Discovery

2640s, relatively recent. After its discovery, it was rapidly distributed around human space, within two decades, sublight spaceships like the Void Traveller had become obsolete, and were either retrofitted with drives, scrapped, or turned into stations in orbit.