History: Adam was once just a man, though not the first man, as his name suggests. (The other interpretation of that name is, of course, a nod to Mary Shelley’s Frankenstein.) He was a member of the Initiative, which tracked demons, an occupation that proved quite hazardous to his health: He was killed by last season’s Big Bad, The Mayor (by ghost/proxy). He also teamed up with season two’s Big Bad, Spike. But after Professor Maggie Walsh resurrected him with a mix of science and otherworldly powers, he became a deadly, highly intelligent adversary for Buffy—he had a uranium core and a huge skewer (a “gift” from another demon).
Adam would also wax eloquent about the nature of human existence, as demons are wont to do. He found imperfections in both demons and humans; where one was physically weak, the other was lacking in substance. So Adam planned to destroy the Initiative and overrun Sunnydale with monsters, and his actions actually brought demons and vampires together. He even did some reanimation of his own, though with diminishing returns.
How’d they bite it? It took a lot to take down Adam. The main Scoobies—Buffy, Willow, Giles, and Xander—used an enjoining spell to imbue Buffy’s body with their, uh, essences. It was the only way the Slayer could become powerful enough to fight Adam, who was, after all, an enhanced demon. The enjoined Scoobies called upon the ancient strength of the First Slayer and… tore Adam’s power source from his body. Basically, they turned him off.