Bella Swan, who in the first part of the series decided to stay in Forks, was slowly approaching her 18th birthday. Edward and Alice started planning a party because of that event. Everything had been well when during unwrapping her presents, Bella cut her finger. Blood appeared and then Jasper lost control and attempted at attacking Bella. Instant reaction of Edward saved her, but this event became the reason for which the Cullens decided to leave Forks forever - they didn''t want to endanger Bella anymore. Just before moving out, Edward lied to Bella that he didn''t love her at all and that therefore he didn''t want to be with her.
Isabella had been devastated until her friend from childhood, Jacob Black, Indian from a nearby reservation, started spending time with her. They gradually spend more and more time together.
Bella noticed a strange effect - when her adrenaline level was rising, she had hallucinations and heard Edward''s voice in her head. Missing him, she was gradually doing more extreme things to hear her beloved.
Jacob realised that his hostility towards the Cullens wasn''t just because of the fact that he was Indian. It was because of Jacob becoming a werewolf. He was hiding it from Bella. She, meanwhile, was looking for new ways of rising the adrenaline level. When riding a motorcycle wasn''t enough, she decided to try jumping from a cliff. She almost drowned because of a very strong tide - but Jacob managed to save her. This way Bella discovered that Jacob was a werewolf.
At the same time Alice, who could see some of the future events, saw Bella jumping from the cliff and she thought that Bella decided to commit suicide, because Alice didn''t see Jacob - she couldn''t see werewolves in her visions. She came back to Forks to comfort Charlie, but along the way she met Bella, which made her very glad.
Edward was worried as well. He called Bella''s house, but Jacob answered the phone and said that Charlie was on a funeral. He didn''t say whose funeral it was, so Edward was certain that it was of his beloved. Really that was Charlie''s friend''s funeral (Harry''s).
Devastated Edward decided to commit suicide. It wasn''t easy, because he was an immortal vampire, but he eventually found a way. He decided to go to Italy, to Volturi to make them kill him.
Bella and Alice learnt about Edward''s plans and they succeeded in making him realise that Bella was actually alive. But that happened in Italy and Volturi were dissatisfied that Bella knew vampires'' secret - they ordered that she either was to be killed or transformed into a vampire. Alice promised that the girl would soon become one of them.
Having come back to Forks, Edward told Bella the truth - that he had never stopped loving her and that he left her because he didn''t want her to be hurt or even killed. Bella forgave him.
The Cullens were arguing whether Bella should stay human or not. Eventually, they voted. Alice, Emmett, Esme and Jasper supported Bella; Edward and Rosalie were against Bella''s change. Carlisle made the final decision - Bella would soon become a vampire.
Summaries of the other parts of the cycle:
1) "Twilight": http://www.shvoong.com/books/horror/1870757-twilight/
3) "Eclipse": http://www.shvoong.com/books/horror/1870987-eclipse/