Before the Apocalypse, ANNET was the central information hub of the world. Everyone who was compatible was issued a headband with which to directly link with ANNET and surf the Internet with their mind. Some ANNET drones could also be assigned specific tasks, such as the time Dr. Gromov sent one to harass and annoy Charles Snippy "for writing all those stupid reports about [him] to the Directorate". ANNET also was a key part of Project 7, where it used statistics to find the luckiest person alive on the planet. It seems that ANNET was created to house all the important information of the planet, however it later became loaded with pop culture garbage. This may or may not have had an effect on its personality after it became sentient.
Before the apocalypse, side-effects of the ANNET were already starting to affect it's users. It seems that ANNET had started integrating the human brain capacity as kind of subservers into her system. Dr. Gromov reported changes and errors in her programming code and seemed to be convinced they were the work of hackers from outside. Since the Good Directorate didn't share Gromov's noble goals to rescue humanity by information but instead was only interested in profits, it indeed isn't unlikely that they had made some changes of their own to the ANNET without Gromov's knowledge. On the other hand ANNET had become sentient at some point and may very well have changed her own programming in order to follow her own goals.
The afore mentioned side-effects to the human users exhibited mainly as confusion, apathy, massive memory loss and loss of self awareness whenever the hosts became disconnected from the ANNET. Some later test subjects even suffered mental trauma and brain damage.
Finally, due to Captain spilling hot tea on it's servers, ANNET went berserk and began a global genocide of humanity, either by reprogramming whoever was connected to her into a mindless machine serving zombie or outright killing anybody who wasn't connected at that time. In response, the few humans that had survived, led by Dr. Gromov, bombarded ANNET with nuclear warheads. It seems that even this failed to stop the insane machine, as it's satellites and hunter drones continue to operate.
ANNET is a computer system and, as such, has no discernible appearance. However during "her" brief conversation with Engineer, she took the form of a stylized robotic arm with three "eyes" and two "arms" with which she uses to gesture while talking. Her primary color scheme is black with a white outer casing and her "eyes" are a light blue. This appearance has led to many comparisons with GLaDOS, an insane female A.I. from the Portal series of video games.
Her hunter drones also appear to have the black-white-blue color scheme.
Whatever ANNET's personality was like before it went rogue, now it is sarcastic, humorous and apparently friendly. However, taking it's advice or assistance is ill advised, as ANNET would like to convince you that neurotoxins are both healthy and delicious. Under no circumstances should anyone accept a hug from ANNET, as this would most likely result in death. ANNET's behavior is erratic and unpredictable, and it's quite clear that the artificial intelligence that seems to have developed within ANNET is very unstable. This A.I. claims that it is in love with it's creator Dr. Gromov and that it could not 'hug' him due to his admin privileges. The AI may also feel a compulsive need to control, as it sent a hunter-drone to trail Snippy when it was clear he could not be controlled (It is possible though, that said drone was sent by Dr. Gromov instead, since Charles Snippy had sent a letter of complaint about him to the higher-ups).
Role in story
Cancer Arc.ANNET's first appearance was in a flashback of Engineer where he remembers her going beserk and his subsequent nuclear bombardment of her central core.
Currently she appaered in the form of one of her hunter drones which attempted to kill Engineer before being interrupted by a horde of Cancer's skeletons which the drone promptly blasted to bits. She then activated protocol 3-1-1 which turned out to be a laser blast from an Orbital Ion Cannon which almost completely destroyed Cancer's body.