There were quite a few factors.
The biggest - a feeling of unity and desire to spread their ideas. Muhammad spent much of his life at war. It's wikipedia, but the best I have at the moment (at work, not with my sources at home) - Expeditions of Muhammad He participated or ordered more than 100 expeditions from 623 to 632.
Early Islamic "armies" were more disorganized groups of fighers, but as they won and united people under the banner of Islam and the idea of ummah or this idea of a brotherhood or nation that all Muslims were a part of, the armies grew and better and better leaders appeared. Organization occurred as well. The Byzantine Empire and the Sassanid Persian Empire were at each other's throats and the Muslims were able to consolidate a force under them before either group took notice. Arabians were horse soldiers as well, meaning they were a mobile force able to appear and disappear just as quickly.
Much of the early success of the empire lies in Khalid ibn al-Walid as well. He was masterful in organizing the troops to make changes.
As the empire grew, they captured places of knowledge. Instead of killing or enslaving the people they captured, they gave them an option...become a Muslim or continue practicing your previous religion but pay a tax, the jizya. Many of the people conquered by Muslims had to change very little except to pay and converts, in the early years, were high. As they took the Persian empire apart piece by piece, they were also capturing some of the world's major trade routes.
The Islamic empire became the place for knowledge from 700AD until the Renaissance. With this knowledge, they added and changed their tactics, implementing the stirrup and other changes. If another army was utilizing it, then the Arabs saw that and adapted it.
Early on, they fought from the desert, leaving it to strike at the larger Byzantine and Persian Empires. Those two powers sent expeditions into the desert, but you can't fight nature, while the Arabs were accustomed to the desert.
The Bedouins of North Africa initially gave the Arabs the most trouble, but after some fighting, they joined up and aided in the conquest of Spain up to France.
Charles Martel is largely the reason the Muslim Empire did not end up stretching through France into the rest of Europe.
There are a couple of great books on the early empire:
Patricia Crone - Slaves on Horses
Patricia Crone - From Arabian Tribes to Islamic Empire
Patricia Crone - Meccan Trade and the Rise of Islam
Hugh Kennedy - * The Early Abbasid Caliphate*
Hugh Kennedy - The Byzantine and Early Islamic Near East
H.A.R. Gibb - The Encyclopaedia of Islam
Fred Donner - The Early Islamic Conquests
Fred Donner - Muhammad and the Believers
These are some great works to get you started.