Anya Jenkins came into existence in the second year of Buffy's high school career. Formerly the vengeance demon of women scorned, Anyanka, Anya was tethered to the mortal coil by her own carelessness.
After Anyanka granted a wish to Cordelia Chase, a teenager who had been betrayed by her boyfriend Xander Harris, the world as Sunnydale knew it changed for the worse. The formerly cool night hangout had become a safe haven for vampires, a dusk curfew had been imposed for the safety of Sunnydale's citizens, the slayer was nowhere to be found and people who should have been alive were very un-alive. Ironically dieing at the hands of her now vampire ex, Xander, Cordelia passed on Anyanka's power centre to Giles. The power centre, the very source of the wish that had turned the world around, was destroyed in a hopeful maneuver by the desperate ex-watcher in a chance to make the world a better place; the gambit paid off... except for Anya. Now a mortal in the form she had disguised herself in for Cordelia's benefit, the thousand-year-old was stuck as a teenager, complete with a teenager's insecurities and lustful urges.
Finding herself strangely attracted to Xander, Anya's awkwardly blunt personality ruffled many feathers as she inched her way into his life. Becoming Xander's girlfriend offered Anya entrance into the 'scoobie gang' and she lent her vast knowledge of the demon sphere.
After high school, Giles opened up a magic shop and Anya found a love for the key player in the capitalist notion of business - money. A sharp business sense combined with Giles' ability to actually interact with the customers left Anya very comfortable in her position in life.
Being left at the alter by Xander tore out Anya's heart (figuratively) and she was reminded why she had become a vengance demon in the first place - to tear the hearts out of unfaithful men (literally). Turning to her vengance demon roots, Anyanka's found joy for infliction was lost and she truly had no place in either world.
Buffy, the vampire slayer, accepted Anya into her tightly knit group of friends begrudgingly, her demon past leading the slayer to be wary of the blunt and sometimes rude ex-immortal girl.
Giles, a watcher and mentor to Buffy, merely tolerated the ex-demon until she offered her aid in researching the forces of darkness and the occult. Finding a wealth of knowledge in the thousand-year-old ex-demon, Giles got past her blunt and overly-explicit statements for the benefit of all.
Spike, a vampire, got along well with Anya, his demonic ways very familiar to the ex-demon. In her time of need, after she had been abandoned by Xander, Anya and Spike shared a brief encounter that allowed both to heal a little from their unique and painful love lives.
First boyfriend and later fiancee to Anya, Xander was the first man Anya had not tried to eviscerate on site in almost a thousand years. Her hopes for a mortal future rested with Xander, the ideas he represented more important to her than the man himself - and he knew it. When he left her at the alter, Anya turned back to her demon ways, hoping to dull the pain of betrayal.
Anya reviles rabbits. They are her most feared creature in all of both demon and human existences. These vile and prolific creatures are the source of much anxiety for the ex-demon.
Willow lost her affinity for Anya - or what little she may have had - when Anya tried to regain her demonic powers after having lost them. Using the fledgling witch without telling her the whole truth caused an alternate (and vampire) version of Willow to reap havoc on Sunnydale, forever driving a wedge between the two.