Arabic was and still is a common language across the Middle East and beyond. Even though spoken Arabic has diverged into different dialects in different regions, the written language has remained relatively constant - restrained in large part by the Quran, since reciting and even memorizing it is considered highly important. So, we have a continuous community from the 600's to the present speaking Arabic, understanding the Quran, and guaranteeing that the interpretation of a given word there today is substantially similar to the interpretation it had originally.

If you're asking about translations, there actually have been many translations of the Quran, including many by people who did speak Arabic. Even in medieval Europe, Arabic was not unknown among educated people - see this translator, for instance, who had studied at an Arabic-speaking university in Spain.