Ash asked Mewtwo who she is.
No one had ever seen a Mewtwo before.
Mewtwo was cloned from Mew by different scientists, who are evil, then unintentionally blew up their lab and killed them after they were shocking her with electrodes and she was trying to push them away.
Mewtwo traveled away and got zapped by lightning in a storm, then fell to the ground and into a cave.
Some Pokemon nursed it back to health.
Mewtwo's new forme is obviously some sort of speed forme.
Genesect were revived from fossils by Team Plasma then escaped.
The Genesect attack New Tork City because it reminds them of their home from prehistoric times and they want to take over. They try to make a nest for themselves.
The Genesect with the Douse Drive gets close to Ash and crew and protects them. He has a little boy's voice and is nostalgic for a flower that is growing in New Tork City that is from their home. He is not aggressive at all and is portrayed as "cute."
Red Genesect is a meany and tells the other Genesect to attack everyone, but it's not really evil. However it can force the other Genesect to fight against their will (which happens with Douse Drive Genesect a lot). As they attack Ash and crew, Mewtwo saves the day.
The rest of the film is about Mewtwo trying to convince the Genesect to go with her - they are unneeded Pokemon born unnaturally, so they should go somewhere else together.
Red Genesect and Mewtwo zoom around the entire city. The worst of the damage is a few smashed walls.
The Genesect nest catches fire because it is feeding into the city's generators. While the wild Pokemon have been attacking the Genesect the entire film (and vice versa), they help put the fire out and the Genesect are touched. They stop fighting.
At the end, Red Genesect isn't listening to anyone so Mewtwo grabs it and zooms up into space. Both lose consciousness. They wake up and watch the sun peak around the Earth, learning that they are part of this world or whatever, then fall back through the atmosphere at uncontrollable speeds. Red Genesect helps Mewtwo as they fall and the two take each others hands. The other Genesect form a web to break the fall, Charizard and Dragonite help, and the Psychic-type wild Pokemon form a bubble from a pond to stop them from hitting the ground.
The Genesect make their home in New Tork City and form a new nest near the flowers.
Mewtwo leaves, but then at the end of the film is watching over the city.
A wild Sableye and Feraligatr were heavily featured in the film. Feraligatr because it was needed to put out the fires, Sableye for no real reason. Perhaps it will have an evolution in X/Y, so they decided to promote it here?
At some point in the film there was a shot of New Tork City on fire with thick clouds of black smoke (one of the characters was describing what would happen if the Genesect nest continued to expand into the city's electrical systems). It looked very much like 9/11. When we walked out of the theater we all simultaneously stated that we think the shot will be cut out of the American dub.