Here is an awesome source.

"Caliphate, the political-religious state comprising the Muslim community and the lands and peoples under its dominion in the centuries following the death (632 ce) of the Prophet Muhammad. Ruled by a c (Arabic khalīfah, “successor”), who held temporal and sometimes a degree of spiritual authority, the empire of the Caliphate grew rapidly through conquest during its first two centuries to include most of Southwest Asia, North, and Spain. Dynastic struggles later brought about the Caliphate’s decline, and it ceased to exist with the Mongol destruction of Baghdad in 1258." - from above.

This next source is talking about the original Caliphate, the Rashidun Caliphate.

Here.

"Abu Bakr served as caliph from 632 until his death in 634. His first major accomplishment was to deal with the problem of the Bedouins (nomadic Arabs). Although some had converted under Muhammad, after his death they rejected Islam and refused to obey Abu Bakr. In 633, the caliph defeated the Bedouin revolt, known as the Ridda, and thereby secured the entire Arabian peninsula for Islam.

The experience served to convince Abu Bakr that Islam needed to expand beyond Arabia in order to be secure. He set his sights on the two neighboring empires he viewed as threats to Islam: the Sassanid Empire to the east in Persia and Iraq, and the Byzantine Empire to the west in Europe, Syria, Egypt, and the Mediterranean Sea. He declared a jihad against the Byzantine Christians, but died before he was able to carry it out."

Abu Bakr also only lived for 2 years after Muhammad. Here is some info Abu Bakr's successor, Umar. Military victories by Umar propelled Islam.

"The second caliph was Umar, another father-in-law of Muhammad, who had been named by Bakr as his successor. His caliphate lasted from 634 to 644. One of his first contributions was to add "Commander of the Faithful" to his title, which was used by all subsequent caliphs. His primary contribution, though, was a series of military victories resulting in the rapid expansion of Islam.

He conquered Damascus in 635 and Jerusalem in 637, both from Syria in the Byzantine Empire. Realizing the importance of loyalty in his new subjects, Umar instituted a policy of religious tolerance in his new lands. This was received gratefully by Jews and Christians, who had been persecuted under the Byzantines. He instituted two taxes, the kharaj for landowners with productive fields and the jizya, which non-Muslims paid in return for the privilege of practicing their religion.

At the same time, Muslim forces were moving against the Sassanid Empire in the east. Once he had secured his place in Syria, Umar succeeded in conquering the Sassanid capital, Ctesiphon, in 637. Turning west yet again, with a Muslim Syria assisting, Umar's forces set out for Egypt. Babylon fell in 641, and Alexandria in 642. Christians have not ruled in Egypt since. Umar continued the policy of tolerance in the newly conquered lands, and Muslims did not force conversion to Islam. They depended too much on the revenue from the jizya tax and the nonresistance of the outnumbering non-Muslims.

Muslims would find that it was not as easy to placate Persia as other conquered lands. By the time Islam arrived, the Persians had become a fiercely nationalistic people. They had their own national religion, Zoroastrianism, and considered the invading Arab Muslims inferior. Caliph Umar, Commander of the Faithful, was assassinated by a Persian Christian in 644. But by the time of Umar's death, the Muslim Empire was second only to the Chinese Empire in size." - same source.

There are other Islamic caliphates too. The Rashidun and Umayyad Caliphates are the only ones that aren't broken up into different sects of Islam. The Rashidun Caliphate is the emergence of Islam while the Umayyad beat the shit out of the Byzantines. The Umayyads are the immediate successors and are responsible for the assassination of Umar.

TL; DR The Islamic empires, religious tolerance and military victories helped Islam dominate the Middle East.