"It'd be like if the British colonies in America were conquered by Native tribes."

Well not quite. It's worth remembering that tribal peoples on horse or camel remained the state of the art in warfare for roughly 1000 years after the conquests, so the disparity is more in the level of state organization than anything else.

The "why" of the conquests is not an easy answer, and it's much debated, partly because our documentary sources for the conquest period are so limited.

For a long time, historiographically speaking, the focus was on Byzantine and Persian side of the question, not so much that they were incompetent but rather that they had exhausted themselves in the latest round of the Byzantine-Sassanian wars.

The Persians, for their part, were basically broken to the point that even before the conquests began in earnest that Arab raids seemed to be pushing Persian territory back, and had been engaged in civil conflict to boot. In the case of the Persians the question is almost more how they managed to hold on as long as they did considering the state they were in.

On the Byzantine side of the coin, I don't think this old "war exhaustion" narrative is held up as well. For one thing, at Yarmouk, the Byzantines, while they might have been war-weary as a state, were still able to field a full army against the Arabs.

Rather I think it's worth having a more nuanced understanding of what "tribal people from the desert" actually meant. These peoples were actually quite familiar with the Byzantines and the Byzantine way of war. The northern tribes of Arabia had been Byzantine clients for centuries. Their trade in the area and the settlement of Arabs throughout the levant meant that the region they were fighting in wasn't particularly strange to them. And as I noted at the top, "tribal people" in this era and context isn't much of a limiting factor as it's nomadic tribal peoples like the Huns or the Goths or whomever who have been smashing settled, established empires for the past several hundred years.

If anything, Islam actually meant that the Arabs were better organized than many of these other groups would have been, and it's the supra-tribal cohesion provided by that religion that is both an impetus for conquest as well as the means by which those conquests are preserved in the face of continued resistance and counter attacks by the former empires.

Two quite good books have been published on this in the past few years that would be worth reading:

Robert Hoyland's In God's Path, which also has the benefit of being quite short.

and Fred Donner's Muhammad and the Believers.

In addition to what /u/CaptBuck wrote, I'm copying a pasting a (not super in-depth) bit I wrote for the question How did the early Muslims get so good at warfare that they managed to defeat the Byzantines and Sassanids back to back, often times being outnumbered?. I also second his book recommendations if you are interested.

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There are multiple factors at play in this.

Firstly, the Arabian Peninsula had not been unified, leading to the perpetual warring between various tribes. If you know anything about Mongol history, than you know what sort of warriors this sort of perpetual warfare can produce. Once united by Muhammad under the banner of Islam, these separate forces were able to focus their abilities outwards. Combined with the tradition of martyrdom and belief in the will of Allah within Islam, you have an effective fighting force. For example, at the Battle of Badr in 624 CE a group of 300 muslims defeated force nearly 3 times larger. This was seen as divine intervention and gave impetus to the Muslim forces. Fighting spirit should not be underestimated.

Secondly, the Byzantines and Sassanids had been weakened by decades of skirmishes and mismanagement. There were a series of wars between the Byzantines and Sassanids between 540 and 629, which resulted in broken armies and destroyed spirits. The situation was ripe for the up-and-coming Islamic Empire to strike at.

Also, the Byzantines and Sassanids relied on Arab client kingdoms, such as the Lakhmids and Ghassanids, to control the Arab populations along the border with the Arabian Peninsula and maintain a buffer zone around their empires proper. When these tribes finally fell, the Arabs of the region had little difficulty shifting their allegiance to the new Islamic empire, facilitating the conquest of large amounts of territory. They had little connection to the overarching Byzantine/Sassanid Empires and ethnically identified with the Arab Muslims.

The Islamic Empire was also, for the large part, benevolent rulers. They did not force conversions to Islam so long as you were Christian, Jewish, or (sometimes) Zoroastrian (although it was favored by institutional constraints like the necessity of paying the dhimma tax if you were a non-Muslim Person of the Book) and originally saw themselves as a separate military caste over the top of the native population. Again, this facilitated the ease of conquest and meant that they did not have to leave large armies behind to subdue restless populations.

This passage from Lapidus that perfectly sums this all up. Im attaching it for if you would care to read it.

The reasons for the relatively rapid success of the Arab-Muslim conquests are not hard to find. The Byzantine and Sasanian empires were both militarily exhausted by several decades of warfare prior to the Arab-Muslim invasions. The Christian populations - the Copts in Egypt, the Monophysites in Syria, and the Nestorians in Iraq - all had long histories of troubled relations with their Byzantine and Sasanian overlords. Their disaffection was important in the cases where Christian-Arab border tribes and military auxiliaries joined the conquerors and where fortified cities capitulated. The conquests, then, were due to victories over militarily weakened powers, and were consolidated because local populations were content to accept the new regime. The conquests were further secured by a large migration of Arabian people. With the defeat of the Byzantine and Sasanian empires, a frontier between populations broke down, leading to a massive movement of peoples from Arabia into the lands of the Middle East.

Most of those topics I had hit on a bit above, but I believe it provides a nice overview of the answer.

If you have any specific questions I can try to follow up later with some more detailed responses.

Sources

• Hourani, Albert. A History of the Arab Peoples. 1991.

• Lapidus, Ira. A History of Islamic Societies. 2002.