Character Analysis
Chancellor Palpatine is a two-faced dirtbag.
As chancellor, he's a cool customer, slimily worming his way to the very top of the Senate and then slowly finding legitimate-seeming ways to lay claim to more and more political power. As Darth Sidious, he's a growling, simpering, prune-faced dictator, willing to go to any lengths in order to fulfill his evil destiny.
Chancellor Silky Voice
When Palpatine is engaging his public persona, he's quite the smooth operator. He knows his audience well, so when he's influencing Anakin, he is a plainspoken dealer of legends and truths, but as chancellor, he is a confident, talented, and inspiring orator.
Because of these skills, he's a master manipulator; he's able to convince the Senate to continue extending his reign as chancellor, as well as granting him more power than any previous leader.
In a scene that strikes us as some powerful political commentary, Chancellor Palpatine informs the Senate about the Jedi's treacherous betrayal (which is a complete untruth) and smoothly announces that he will fix everything by becoming Emperor, to Padmé's immediate dismay.
She watches as the Senate reacts enthusiastically to the announcement, and remarks:
PADMÉ: So, this is how liberty dies. To thunderous applause.
It's a testament to Palpatine's ability to completely bewitch people—he's able to convince believers in a system of democracy to adopt a ruthless dictator to lead them.
Most of the time, though, we see his skills as a smooth-talking operator when he's trying to lure Anakin over to the dark side. Using both his system of political spies and his powers as a Sith Lord, he learns that the key to converting young Skywalker is to use his fear about losing Padmé in childbirth.
So, he launches a subtle mission to turn Anakin away from his Jedi support system while hinting about the dark side's superior abilities, which works like a charm. He relates the tale of Darth Plagueis, the Sith Lord who learned how to defeat death … and, from then on, Anakin is putty in his hands.
Darth Insidious
When Palpatine is able to inhabit his Sith alter ego, Darth Sidious, he no longer has to hide how truly evil he is. In fact, he revels in it, gleefully embracing how good it feels to just ride the current of hatred and anger without any need for inhibitions.
At one point, while shooting lightning bolts from his fingertips at Mace Windu, he cackles triumphantly: "Power! Unlimited power!" and smiles as his opponent falls to his death.
As Darth Sidious, he knows no loyalty too great for betrayal, and all motivations are his own. In fact, by having a Sith alter ego, he's able to manipulate events behind the scenes in order to set things up for his more benevolent persona, Chancellor Palpatine.
In both The Phantom Menace and Attack of the Clones, he's able to orchestrate political upheavals, only to have the victims approach him for help, not knowing that he's actually the mastermind behind it all. This is how he's able to get himself elected Chancellor and then granted emergency wartime powers, which are extended long past their intended duration.
He even treats his apprentices like disposable tools, abandoning one as soon as he finds one more powerful to bend to his will (poor Count Dooku). Later on in the series, he tries to make Luke kill Darth Vader in order to take his place, even after all of their years of evil deeds together. That's pretty harsh, man.
But, one of the overarching themes of Revenge of the Sith is that people with power fear losing that power, and that fact is all too true for Palpatine. He's pretty aware of his vulnerability as the person in charge, and as such, he is constantly on the lookout for someone more powerful that he can rope into doing his bidding.
Supreme Bad Guy
Ultimately, the importance of Chancellor Palpatine/Darth Sidious is that, in contrast to Anakin/Darth Vader, he's actually truly and completely evil. There aren't any redeeming qualities or extenuating circumstances that made him turn to the dark side.
No, he's in it for the pure joy that it brings him to have that power at his fingertips (literally). He's the true, number-one bad guy throughout the entire Star Wars mythology, which gives the stories a continuity that might not otherwise be possible.
Chancellor Palpatine/Darth Sidious' Timeline