I have never gotten through a trilogy so quickly, at least not one where all the books have been published. I had a brief flirtation with the Children fo the Lion series by Peter Danielson, but that was far more than a trilogy and it took some time to get through the first 2 books.
I am not sure if it is the subject matter (dystopian future) or that the characters and plot are so interesting, or it could be Roth's writing, but I devour all three books in about 4 days.
Insurgent takes up where Divergent left off, but the ante has been upped way up. Tris's previous faction, Abnegation, is at the heart of the story because Erudite's leader is using Dauntless as the army to take the entire faction out. Even though faction before blood is at the heart of the factions, or at least has become in recent years, Tris cannot slough off her abnegation training and heart so easily. She is also divergent and the only person ever to come out of the simulations with three choices: Dauntless, Abnegation, Erudite. She is a very unique person, not to mention that she combines the elements of all three -- fearless, intelligent, and selfless -- in a brand new way and is immune to the simulation injections. She can control what happens and cannot be controlled by Erudite, which makes her a wild card in Erudite's plans, one that the cannot guard against.
Four, also known as Abnegation leader's son, Tobias Eaton, can be controlled, though he is also Divergent, and Tris must face off against him and all her friends in Dauntless. Erudite has a plan to get rid of her, thanks to Peter, Tris's nemesis in Dauntless, and her fear of drowning in an enclosed container is given life to take her out of the game. After all, Divergent must be eliminated in order for Erudite's plan to work.
As the Abnegation faction is attacked and many of its people eliminated, Tris must break find a way to break out of the cube and save the Abnegation people, including Four's father, whom she loathes, in order to get the truth out about the reason why factions were created and why they must live their lives within the confines of what once was Chicago, a truth that Erudite is willing to kill to protect.
Veronica Roth really turns up the heat in the Divergent trilogy with Insurgent and she brings out the interconnected layers and more characters, creating a dense onion of a world where friendships are tested and Tris's heart are laid bare. Roth adds complexity upon complexity and changes the game in fundamental ways for Tris and the faction divided world in which they all live. Sacrifice, truth, duplicity, control, manipulation, and fear add texture to a landscape already divided and fighting for its survival as the workings the workings of the remaining factions are brought to light.
Insurgent lays the groundwork for the final book of the series with a stunning truth that places Tris, Four, and their friends and enemies into a much larger world with so much more to lose -- and to gain. Insurgent is still 5/5 in writing, characterization, plot, and appeal.
I would also like to mention that although there are children killing children (and adults killing adults) the Divergent series shares nothing much with the Hunger Games books.