Arab culture, by and large, spread with the Muslim conquests. As you may know, there were several Muslim empires that covered huge expanses of land, from the greater Middle East to swaths of North Africa and into parts of India and Europe (famously Spain, but the cultural influence of the Ottoman Empire also reached into Eastern Europe).

But the main question is: why did culture and “race” spread along with the conquests? There are plenty of example of empires not leaving half the cultural mark as the Arab/Islamic Empires. The majority of Chinese, Russians, and Persians for example don’t self-identify as Mongols for example. The big reason Islamic culture spread so well is due to administrative/religious dictates that allowed foreign cultures and religions to survive under Islamic rule but encouraged conversion.

To start with the religious aspect, there’s several laws in the Qur’an that dictate how to treat non-Muslims living under Muslim rule. The famous jizya is a tax to be paid by “people of the book,” who are classically understood as Jews and Christians but which has also been applied to Hindus and Zoroastrians, among others. By paying the jizya, a household is able to maintain their religious identity and also be exempt from other Muslim-only obligations like military duty. As you can probably infer, this is a handy way to prevent religious strife and keep communities of other faiths under your rule, while simultaneously being an economic incentive for members of those communities to convert.

While forced conversions certainly did happen, by and large the spread of Islam happened due to these “soft” means of incentivizing conversion. Not only did being Muslim ease your tax burden, it also gave opportunities for advancement in political and social standing, as many government positions were only available to Muslims. Sometimes these restrictions were codified in law and sometimes it was only discrimination carried out in practice, but in either case being Muslim made it easier to network and trade. A huge amount of conversions also took place purely through the power of trading, for example the Swahili states of Africa by-and-large follow Islam purely because of trade influence. Inter-marriages between Arabs and non-Arabs were also not uncommon, and that does a great deal to influence culture.

Another other reason that goes hand in hand with this is that the Islamic Empires, generally, had a relatively non-centralized form of government that allowed local cultures to survive in tandem with Islam.

Becoming Muslim also had huge cultural implications — Arab culture and Islamic culture are closely tied together even today, even though a few of the most famous Islamic writers and poets weren’t Arab. To understand Islam, one inevitably comes into close contact with the culture of Arab tribes at the time of Muhammad, along with the Arabic language; a tradition of learning the entire Qur’an by heart has existed from the beginning of Islam to this today. Muslims (especially children) today are encouraged to learn the Qur’an by heart, even if they don’t know the language.

Especially as time wore on, Arab culture had huge prestige, and conversion allowed access to that prestige. As a Muslim, you would be able to identify yourself with figures of huge cultural influence — the famous singer and “inventor of manners” Ziryab, the greatest traveler to ever live Ibn Battuta, and other huge figures in the fields of medicine, engineering, linguistics, and mathematics.

This is by no means a complete, or even very complex answer, but I hope it answers your question.