Uthman was chosen as the successor of Umar on the basis of his being a weak, and therefore less objectionable, candidate for the Caliphate. In this he had the misfortune of succeeding the vastly more talented and accomplished Umar. This paired with a slowing in the rates of conquest by the Arab armies, so while the maxium extent of the empire wouldn't be reached for almost another 100 years, the easy, rich lands of the Levant, Persia, and Egypt had all been successfully conquered while Byzantium would not fall. The result was something of an identity crisis among the Arabs now living in the provinces between a traditional Arabian mode of life predicated on conquest and the "new normal" of overseeing the conquered territories as administrators.

Some of the provinces handled this better than others and this was a mix of family ties, Arab tribal politics and religious issues. Uthman, for instance, sought to unify the various readings of the Quran to produce an authoritative version, the Uthmanic Codex, which remains the "standard" Quran but he was resisted in this particularly by the people of Kufa which was a major settlement in Southern Iraq. Likewise, while he had the support of the Levant under his talented relative Muawwiyah his rule was resented by the Arabs in Egypt and also by the Medinese who thought that his tribe, the Ummayads, should not be consolidating their rule given their tribes resistance to Muhammad (although Uthman himself was an early convert.) Ali, Muhammad's son-in-law and nephew, became the symbolic, if not actual, leader of the discontented parties.

Within this context, a group of soldiers from Egypt returned to Mecca where they understood their grievances would be heard. Upon discovering that their leaders were actually going to be executed they broke into Uthman's house and murdered him.

Ali was then proclaimed Caliph by this group of plotters but was immediately met with rebellion by Muhammad's wife Aisha and two of the companions of the prophet who supported her based in Basra, while Ali was based in Kufa. Muawwiyah, the governor of Syria, also rebelled, which produced the First Fitna or Islamic Civil War. Worth noting is that from the Ummayad perspective, Uthman was the third Caliph and Muawwiyah the fourth, so that Uthman was the first "Ummayad" Caliph. Later Muslims would reckon that Uthman and then Ali were the third and fourth of the four "rashidun" or "rightly-guided" Caliphs while Muawwiyah would be the first of the Ummayads.

Source-wise, Marshall Hodgson's The Venture of Islam gives a good overview of these events.