There were two "Trek Tech" as I like to call them, that were vital in defeating Nero.
1. Warp Drive
2. Red Matter
Starting with Warp Drive, this was used through out the plot line of the film. It gave them the ability to travel at the speed of light in order to reach great distances in a short amount of time. They were able to pin point exactly where they had to slow down in order to arrive where they needed to go. They had to first travel from Earth to a far off planet called Vulcan in order to respond to a distress call. Hate to quote Star Wars while talking about a Star Trek movie (I was always more of a Star Wars fan myself), but
They come into an ambush by the Romulans, who were from the future (long story) who then destroy Vulcan but we'll get to that later on.
The Romulans then head off towards Earth, using warp drive of course, to destroy it. The enterprise decides to chase after them but instead of showing up at Earth, they stop in the outer moons of Saturn for cover.
So warp drive obviously has a huge impact on the movie and while yes it seems so fanciful, it's not quite reality. Vulcan isn't even a planet so if it was then it would be light years away. Which means that time would be shifted very dramatically after a jump to Vulcan. It could be years to everyone back on Earth while only a few minutes to them.
Now on to the red matter. Its even futuristic for the futuristic Star Trek scene. When reacted, the red matter creates a black hole.
Now back to Vulcan, the Romulans drilled a hole to the center of the planet and would then drop red matter into the center, causing a reaction, causing a black whole which would destroy the planet.
That's what they were planning to do to Earth as well. Spock and Kirk beamed aboard to steal the red matter and save their captain. They then crash the red matter into the Romulan ship creating a black hole.
I have no idea if this red matter can be created because it's from the distant future but who knows it could be possible.