In The Ornament of the World, Menocal explains that Muslim Iberia had many profound lasting impacts on the West. I will provide a brief overview of some of the main impacts, but note that there are many right answers to this question.
One of the main points Menocal highlights is that the West’s economic reliance on Muslim Iberia’s trading economy led to commercial and cultural exchange. This exchange ultimately transformed Western culture.
Menocal writes in the sectioned titled "A Brief History," that under Muslim rule, the Iberian Peninsula was home to “the commingling of languages, religions, and styles of every sort-food, clothes, songs, buildings” (41). When cultural ideologies intersect like this, ideas spread, and Muslim culture was inevitably brought to the West. For example, Westerners translated scientific and philosophical writings from Cordoba’s libraries to bring these ideas to Western scholars.
An interesting cultural cycle of sorts occurred in the Middle Ages, when Westerners studied intellectual and scientific ideas from Muslim Iberia. Muslim scholars had been influenced by classical Greek thought, which the West had lost the ability to understand in this period. Through cultural exchange with Iberia, Western states rediscovered classical ideologies. This rediscovery of classical thought was the root of the transformative Western Renaissance.