There are different interpretations about the Camel War. Who started this war and why? Which side of the war was the aggressor?
The leaders of both sides were from the companions of the prophet Muhammad (PBUH).
You're thinking of the First Fitna - the Battle of the Camel was a significant battle therein.
Caliph Uthman was assassinated because his and his predecessor's policy of appointing family and those with tribal affiliations to important posts was massively unpopular (altho overall Uthman's reforms were effective). In his place, Ali ibn Abi Talib was appointed the new Caliph by an uneasy alliance of rebels and religious leaders - and this was unacceptable to the very same family members and those with tribal affiliations that were put into positions of power (most notably Muawiyah) by Uthman and his predecessors.
The casus belli put forward by Muawiyah and those allied to him, including Aisha, is that they would only accept Ali as the new Caliph if he could bring Uthman's murderers to justice. Ali could not or would not, and so began The Fitna - the first Islamic civil war, who's effects are still felt throughout the world today.
The Battle of the Camel came on the heels of the Nakithin (a name given to the faction including Aisha that was allied with Muawiyah) moving in to sack Basra, a city nominally allied with the new Caliph that also happened to be the location of a large treasury. Whoever took Basra would have gold and supplies - neither side could afford the other to have the city. They negotiated a bit, and then had at it, with Ali and his allies getting the upper hand in the end.
This is one of the most contentious parts of Islamic history, and the origin of the Sunni/Shia split, so be wary of religious-flavored crackpottery when googling around for more info. The Wikipedia entries are pretty closely monitored and good sources, with plenty of references.