Ibadis were formerly part of the army of Ali. Later, after the death of Uthman, Muhammad's widow so was enraged at Ali for succeeding Uthman without bringing his murder to justice and attacked Ali's army in Kufa at the Battle of the Camel. She lost and part of her army was taken prisoners.
After this, Uthman's governor of Syria Muʿāwiya attacked Ali again at the Battle of Siffin. These were major civil wars with tens of thousands of experienced military units dying on the battlefield. So many that when Muʿāwiya was about to be killed by Ali's army, he had his soldiers affix Qurans to their spears to force arbitration. Ali appointed an arbiter, but his army, who was from Kufa (near Baghdad) rejected him and appointed their own.
During the arbitration, Muʿāwiya's arbiter convinces Ali's arbiter to disavow Ali as caliph, and accept Muʿāwiya as the new caliph. When Ali's representative and Ali himself accepts, Muʿāwiya becomes the first caliph of the Umayyad dynasty. Unlike the four before him up to this point, he is unelected, and secures his caliphate with military power. Part of the arbitration required him not to name his son as successor. He does anyway. It is from him that the Sunni Umayyad Caliphate originates.
Ali's army, incredulous at the turn of events, begs Ali to fight Muʿāwiya but he refuses. Ali challenges them, saying they were the ones who recommended this arbiter, so they yield and say it was a sin, but that they repented and so must Ali. Instead, Ali takes an army of loyalists and crushes this insurrection at the Battle of Naharwan. Ibadis identify with the Naharwanis, who were the precursor group. However, one group goes to Kufa, the Khawarij, and the other to Basra after accepting Ali's terms of surrender which only require them to take his amnesty. They do. These loyalists become the Shia.
Later, Khawarij from Kufa kill Ali as he prostrates in prayer with a poisoned sword. The response from the Umayyad dynasty is to attempt to kill all those in Kufa and Basra that they deemed responsible. So they chased the Ibadis all over Arabia, but as Basra was formerly a Persian port, the Ibadis are able to escape to the sea. However, their leadership becomes pushed into Hadramut in Yemen. Just as the Umayyads are about to strike the final blow, a revolt breaks out in Syria and they are forced to leave. Ibadis accept terms in which they agree to pay zakat to the Umayyads and thus become a tributary state. From Yemen they move north into Oman, the bordering state, where they remain to this day.
Ibadis become known as master ship builders, and become responsible for Arabian trade with East Africa and India. They chop down trees for boats in Kerala, India, trade goods with Tanzania from their port in Zanzibar, and in Oman institute massive irrigation projects that remain functional to this day. Unlike other Muslims, they don't try to convert their trade partners. But by example, many foreign groups adopt Ibadism.
Later, the Portuguese seize the East African coast and Oman itself, holding it for a very long time after taking control of the seas from Oman. It is not until Ottoman times that the Portuguese are pushed out, and as a result Omanis become very exposed to western ideas. Ibadis push out the Ottomans, who are successors to the Abbasids who are successors to the Umayyads, and institute self government. They revitalize the trade routes and build up an Omani Empire which is slowly chipped away at through being replaced in its foreign colonies by the Germans and British. Succession struggles split the royal line between Zanzibar and Oman, and Zanzibar is overthrown by a massive revolt, forcing most Arabs and loyalist Tanzanians into Oman.
This made Oman a multicultural community of different sects of Islam guided by two people - the nearly secular King of Muscat, and the conservative religious Imam of Oman. The Imam of Oman guides the religion, while the King of Muscat handled trade. However, in the 20th century, the Imam declares a jihad on the king, and the two fight. Although the king has the upper hand, socialists from Yemen start to turn the war in the Imam of Oman's favor, who in addition receives support from Saudi Arabia.
The King's problem at the time is a lack of modernization. These closed communities mean infrastructure development has been backwards since colonial times. So in 1970 his son overthrows him, defeats the Imam of Oman, moves the capital to Muscat itself, and Ibadis generally follow and settle there as well. He does this with extensive help from the British Empire, who rewards him by modernizing his country up to their standards.
As a result of this long history, today Oman is one of the most modern, moderate, tolerant nations in Arabia, and unlike every other country in the Middle East does not face any kind of domestic insurrection. Because the coup was bloodless, there was nothing to avenge, and instead the country was able to focus on economic development. It is peace, not war, that is common in Oman.
The best example of this would be the fact that although they are a member of the Gulf Cooperation Council which includes Saudi Arabia and the United Arab Emirates, they do not at all participate in sabre rattling with Iran. On the contrary, they are one of the few countries to trade freely with them, and the three countries generally control the straight of Hormuz through which most oil in the world passes through.
Religious wise, this can be attributed to a rejection of the blood feuds between Sunnis and Shia following their experiences in the first Islamic civil war. Furthermore, they adopted pacifism unlike the Khawarij who were eventually wiped out to the last man. Lastly, they devote themselves to the friendship of their community, positive relations even with those they disagree with, and caution - not fear - when dealing with the unknown. Lastly, they request nothing of Allah during prayer. They offer only praise.
To Ibadis, this is based in the traditions passed down from the Prophet Muhammad. They as well reject many of the Sunni and Shia ideas so often criticized in the west. They don't see the Sunni caliphs as particularly different from any other Muslim, nor Shia feudal dynasties as significant either. Ibadis say anybody can be a leader.
I'm sure that's more than you asked, but I wanted to give you all the information you could want on this subject.