The Middle Ages are often called the "Dark Ages," but in fact there were many great discoveries in science. Many of these resulted from recovery of information that had been preserved by the Arabic speaking peoples. The translation of works from Arabic into Latin took place mostly in the monasteries and in the universities which were church-run. Often it was the monks and teaching clerics who first applied what they received through those translated sources.
The Arab world introduced the number Zero to Europe. It was originally a solar hieroglyph. From the Arabs also came the decimal system, which aided advancement in the sciences. The works of Al-Khwarizmi (Alghorismus, from whom the term "algorism" was derived) became available to Europeans during the Middle Ages. His work laid the foundation for algebra and complex mathematical problems, such as square roots and complex fractions. Many of his books were translated into European languages. Trigonometric work by the Moorish scholar Alkirmani of Toledo, Spain was translated into Latin (from which we get the sine and cosine functions) along with the Greek knowledge of Geometry by Euclid. Along with mathematics, masses of other knowledge in the field of physical science was transferred.
Islamic contributions to Science included Ibnul Hairham’s works on Optics, and the Principle of Pendulum, which was used to measure time.
The basis for Chemistry was the Arabic study of alchemy. Alchemy explores the constitution of matter. Jabir ibn-Hayyan (Geber) was the leading Arab chemist. A great number of terms used in Chemistry such as alchohol, alembic, alkali and elixir are originally Arabic words.
The field of Medicine also developed significantly in the Middle Ages. Every major city had an hospital, but none as great as the hospital at Cairo, Egypt which had over 8000 beds, with separate wards for fevers, ophthalmic, dysentery and surgical cases. Hundreds of medical works were translated into Latin from Arabic.
Many of the institutions we take for granted today emerged in the Middle Ages: banking, hospitals, and universities. Monasticism served the needs of the general populace, not just the monks. Monastery gardens produced foods and herbs that were used to feed and heal. Christianity stimulated great works of architecture, literature and fine art. It was far from a "dark" time, but it ushered in a relatively dark period, especially in Italy - the so-called "Renaissance" which was full of political strife, bloodshed and hedonism.
Related reading: The Monastic Life