Fans of Dragon Ball have watched Trunks grow up from a bouncing baby boy to a skilled Saiyan warrior. He's shown to be just as capable of harnessing his Saiyan abilities as his father Vegeta before him. He's passionate, protective of his loved ones, and has a good head on his shoulders. He's also a skilled swordsman. Unlike the other Saiyans in the group (with the exception of Goten), Trunks uses a weapon in more than one situation. He and Goten even go on to open up their own school, the Kikoukenjutsu Sword School, after the end of the manga.
Where the sword we see Future Trunks use came from isn't exactly clear. There was a movie, Wrath of the Dragon, that attempted to explain its origin. In the movie, Trunks receives the Brave Sword from a being called Tapion, who had been sealed in a music box until it was wished open via the Dragon Balls. Tapion even says at one point that it was always meant for Trunks to own it. This could be a reference to Future Trunks. However, without knowing if the movie is canon, this is purely speculation, though it is highly implied. If we stick to just the original manga canon, this sword could not have come from Tapion because everyone was killed by the Androids, and so the music box was never received and Tapion was never released, but its origin is never explained otherwise.
In the movie, Trunks is shown as having an interest in swords -- playing with a toy version early on. This interest continued into his adulthood, where he and Goten decided to open up their own school after Gohan's book about advanced martial arts was released. It was here that they learned a material called Katchin could be cut, even though it was said to be one of the hardest materials in the universe. They both trained and opened their school as adults, which played a major role when remnants of the Frieza Force attacked Earth.
In the Super manga, Future Trunks is using the Z Sword after receiving it from Future Shin and Future Kibito. He uses the sword in a fight against Future Debora, but it gets turned to stone when Dabura spits on it. This causes Future Old Kai to die. But it is not the first time one of Trunks' swords is broken, as shown in the anime when it's broken during his battle with Fused Zamasu.
With all of this in mind, what can the sword do? Well, by itself, it's nothing special. Three members of the Frieza Force have been shown to wield it without noting anything remarkable about it. However, Trunks is able to use it as a conduit for his energy, wherein he can increase the speed and power of his attacks. In Super, he's able to infuse it with so much power that it turns into a greatsword of energy.
The hardness of the blade is ambiguous at best. It's shown to be able to slice through Frieza in Trunks' first appearance, block Goku Black's Energy Blade attack in Super, yet it couldn't cut through Goku's finger or even Trunks' own hand when King Cold threw the weapon back at him. This could be explained by Trunks infusing the weapon with energy, and when the weapon is not being used in such a way, it's easily blocked. But then this is also countered by the fact that Android 18 was able to block the weapon with no problem with just her arm. The whole thing is just a big mess.
The designs of the sword change throughout its depictions in the games, anime and manga. In the original series, the sword has a metal guard with black leather wrapped around the hilt. In Super, the hilt is green with a silver guard. This implies that Trunks uses several swords throughout the canon, which makes it seem like Trunks probably has extras laying around, and that it isn't some mystical weapon that only he can use. Considering he runs a sword school, there would be plenty lying around, after all. This brings a focus on how Trunks uses the sword rather than what the sword itself can do.
Overall, the mystery of Trunks' sword may remain just that. Unless Toriyama comes out and clears the air about the original sword's origin, we may never know what the deal is. The alternate timelines, universes and time-traveling do nothing to help us better understand. Sure, they've tried to explain it, but it doesn't really line up with the original canon. But, this also just brings Trunks' own abilities to the forefront: He's able to take a regular sword and do great things with it simply by using it to channel his energy.
