Short answer
The Golden Age, roughly from the 8th to the 13th century, was a period when Muslim scholars in Baghdad, Cairo, Córdoba and elsewhere led the world in science, medicine, philosophy and the arts, and preserved and extended the knowledge of earlier civilisations.
The fuller answer
Al-Khwarizmi's work gave us the word 'algebra'. Ibn al-Haytham laid the foundations of modern optics and the experimental method. Ibn Sina's Canon of Medicine was the standard medical text in Europe for centuries. Al-Zahrawi advanced surgery, and Muslim astronomers named many stars still known by their Arabic names. Fatima al-Fihri founded a university in Fez in 859.
The scholars of the time translated Greek, Persian and Indian works into Arabic, and later their own works were translated into Latin and shaped the European Renaissance. Many of these scholars were driven by a religious call to study nature, and they included Muslims, Christians, Jews and others working together.
This answer follows the mainstream Sunni understanding and is general learning, not a fatwa. Where Muslims differ, the answer says so. Have a question of your own? Write to us.