The synopsis tells us that the film begins a few years after the end of ATTACK OF THE CLONES and is near the conclusion of the "Clone Wars" themselves. Hayden and Natalie are still hitched and Ewan is still at work trying to get to the bottom of who ordered the clones made and if there is a connection to the mysterious Sith. Apparently, Count Dooku (YEAH! SARUMAN IS BACK) is still fucking the galaxy up hardcore by waging his war all over the Republic, thus scaring and terrorizing the galaxy. This war between the Confederacy of Independent Systems and the Republic has left a wave of destruction that is literally ripping the galaxy asunder leaving destroyed and devastated planets and lives in its wake.
Palpatine, in order to restore order where there is only chaos, creates a New Order called the Galactic Empire in the aftermath of all this destruction, to heal what has been broken. While that little development happens, Padme squeezes out twins called, shockingly enough, Luke and Leia. However, the infants are separated to be brought up unaware of each other's existence. (YEAH I REALLY WANT TO KNOW WHY TOO!) It seems that Anakin is continuing his descent into darkness by joining Palpatine's side through all of this, where Palpatine can further seduce and bring him to the dark side. (Does Anakin become Palpatine's Jedi Bodyguard?) Ol Kenobi, of course tries to turn Anakin back onto the path of the good guys. The Jedi Order gets destroyed leaving only OB1 and Yoda - and from the look of this thing, the last sentence is: "... a new reign of terror is ushered in with the Empire's rule and Palpatine's move to declare himself the Emperor."
Dont't forget to also check out: Star Wars: Episode III - Revenge of the Sith