Of all the main characters of the story Cersei is easily the most cliché. She fits the stereotype of the wicked queen so perfectly it even includes lesbian sex. Hers is more of a character study than anyone's. Her story is more advanced by what she is than what she does.
Understanding her personality is easy. She is obsessed with power. All things considered, she really doesn't exhibit any redeeming characteristics. Her tv iteration wherein she loves her children is very unlike the book character. Her love of Jaime too is also exaggerated in the show. She loves them only to the extent that she looks upon them as extensions of herself.
All that being said that doesn't mean there is no depth to her character. In fact, her 'character' is what makes her important to the story. (Sorry for the pun.)
So what is her character?
To start, we have to acknowledge how limited her presentation is in the early novels. GRRM has even admitted in an interview that he had originally intended for her to not have any POV chapters at all. The fact she is presented strictly through the eyes of Tyrion and Sansa is important. It helps to establish her as the villain. Her motives are mysterious and she comes across as spiteful and manipulative. Yet at the same time she is often seen as stupid, vapid, and even paranoid.
Spiteful and manipulative she is, she is none of those other things, although one could argue that she is developing a paranoia complex. What is most interesting about her is a fact just about everyone appears to have missed. The more she achieves her goals the less power she has.
It is very much a morality tale and it very deliberately mirrors JRR Tolkien's Silmarillion. Specifically the story of Numenor where the Numenoreans' lives shrank the more they tried to make them longer. The irony of Cersei's story is that she never had more power than when she was Robert's wife. After she killed him she only lost power. First to Tyrion, then to Tywin, then to the Tyrells, and finally to the High Sparrow. All her plans go to hell, and even the ones that work the way she wants only result in her becoming more helpless. This causes a vicious cycle wherein she seeks to reclaim the power she once had only to lose more.
I have mentioned regarding the Others and Lady Stoneheart that ASOIAF is essentially a morality tale against the desire for revenge. Cersei also embodies this concept. It is her hate and spite which leads directly to her fall. Her hate and resentment of Robert is what made her cause his death. It is her hate and resentment which makes her turn the Tyrells into enemies. And it is her determination to obtain revenge upon those who she blames for taking her power from her, the Three Heads of the Dragon, that causes her to instigate the attack which will lead directly to her brother Jaime's death.
I will explain more fully in my article on Jaime.
Cersei will consciously choose revenge upon her enemies over her humanity. Further, she will encourage Illyrio Mopatis and the Slave Masters to attack Westeros even as Jon and co fight to save the world from the Others. This is what makes Cersei the true ultimate villain of the story.
Here I have to give a shout-out to Order of the Green Hand. They helped me apprehend something I have known for years but never really thought about. I am talking about the clear and obvious mirroring between Dany's story line and Cersei's. People have used this as evidence that Dany will go 'mad queen' just as Cersei has. But what they have failed to notice is that Cersei and Dany's story lines swap just like Arya and Sansa's. More accurately, they run in opposite directions.
This touches on the point I just made. Cersei starts off as all-powerful, or at least as powerful as she ever gets. Dany starts off as powerless. Dany obtains more and more followers as the story progresses. Cersei, less and less. And so on. To say this rules out Dany ever going 'mad queen' would be fatuous. But what it also rules out is something else that the TV show harped on. Dany is not and will never be obsessed with power. Dany is the anti-Cersei.
But the mirroring runs deeper than that. The events that take place to the two of them mirror each other to a degree above that of any other characters in the story. The matching is not absolute, obviously. But they are real. Here is an (incomplete) list in no particular order:
1) The Harpies The Sparrows
2) The Green Grace (Galazza Galare) The High Sparrow
3) The Shavepate (Skahaz mo Kandaq) Osfryd Kettleblack
4) Victarion Greyjoy (burnt arm) Jon Connington (grayscale)
5) The Fighting Pits (cultural center) Sept of Baelor (religious center)
6) Slavery Caste resentment
7) Barristan Selmy Jaime Lannister
8) Meereen Kings Landing
9) The Slave Masters The Starks
10) Fire for Death (Fighting Pits) Burning the Sept of Baelor
11) Strong Belwas The Mountain that Rides (Gregor Clegane)
12) Daario Naharis Osney Kettleblack
13) Yunkai The Golden Company
14) Hizdahr zo Loraq (F)Aegon "Targaryen"/(Blackfyre)
15) Wandering the Dothraki Sea Walk of Shame
16) Battle of Fire (Siege of Meereen) The (Almost) Fall of Kings Landing
17) Reznak mo Reznak Varys (the Spider)
18) Quentyn Martell Tommen Baratheon
19) House with the Red Door The Red Keep
The points of similarity are hardly exact. Nor are they meant to be. The differences point to how each woman is on an opposing path. Frequently each point of similarity has an equal point of conflict. For example, Dany's burning the Masters in the Fighting Pits solidifies her rule of Meereen, whereas Cersei's destroying the Sept of Baelor ruins her control of Kings Landing.
Also, in some pairs the significance of one to the story is greater than the other, such as the Mountain vs Strong Belwas.
What demonstrates this better than any is the House with the Red Door vs the Red Keep. To Dany the House represents an idealized childhood that may or may not have actually existed. To Cersei the Red Keep represents an idealized future which she will never obtain, despite the fact she has lived in it for close on twenty years.
I won't go through each one because it would take too long. There are probably others I haven't thought of.
All are significant, but none more than the outcome of the battles for the cities. The Battle of Fire, or 2nd Siege of Meereen, will end in a surprising victory for Barristan Selmy and Meereen. This will end all efforts to take Meereen by force. Instead, the Masters will try subterfuge, bribing Victarion, the Treason for Gold, to turn on Dany.
The almost fall of Kings Landing is dealt with in the article on Faegon.
The end result of both is a Fire for Death. Dany will execute by dragonfire all those who had turned on her: Hizdahr, Reznak, Skahaz, Galazza Galare. I only exclude Victarion from this list because I am sure he will die before this.
Cersei will blow up the Great Sept just as she does in the show. One difference will be that Randyll Tarly will also be inside it. The High Sparrow is going to name Randyll the new Grand Captain of the Faith Militant. He will become Margaery's jailer.
Tommen will die by his own hand, though I don't know if it will be because he throws himself out a window. It does seem likely.
The greatest change between Cersei's book story and her TV version has to do with her future. The conquest of Kings Landing will happen long before the end of the story. To start with Daenerys will be hesitant to attack the city because Tyrion will warn her that it is a giant trap. Cersei will put wildfire underneath the whole thing.
Arya will almost certainly attempt to assassinate Cersei before too long.
Cersei will manage to put her off long enough for the Mountain to save her.
She will do this by betraying Littlefinger This will lead directly to Littlefinger's own death. I'm guessing Sansa will have Brienne throw him out the Moondoor.
This will also be when Arya obtains the Catspaw Dagger.
Eventually Jon, Arya, and Dany will decide that the situation regarding Kings Landing cannot continue. Probably after the Wall falls and the Others march south. They will try to take the city before Cersei burns it down, but they will fail. Cersei will escape, probably with the help of Sallador San. Jaime, it must be said, will not go with her.
This is where the opposing story lines will find their last parallel. Just as Daenerys began as a homeless fugitive fleeing "assassins", Cersei will also become a homeless fugitive. Though the ones chasing her will be more real. Ironically, her own brother, Jaime, will be one of them. In another point of similarity, Cersei will be sheltered by Illyrio Mopatis just as Dany had been.
Thus her fall into total powerlessness will be complete. She will be caught, unlike Dany, and returned to Westeros. Dany began in a comfortable home, the House with the Red Door. Cersei will end in a cell on Dragonstone.
She won't be killed immediately, however. The Three Heads will wait until the end. How and when this happens is not certain to me. It is still a possibility that Tyrion might be the Valonqar. If so than it will take place after the Long Night is over. A further irony is that he will do it not out of hate, but pity. Cersei will be quite mad by then.
If, as seems more likely, Arya is the Valonqar then it will take place before the final fight at the Heartree. I fully expect that Arya will emulate the words of Maggy the Frog. And she will strangle her to death so that she feels herself dying.
Arya's story also mirrors Daenerys, though not to the same degree. Hers is more a parallel of the journey and less on the details.