A Great School was one of five of the highest learning and advanced training centers of the Corrino Empire. Each of the Great Schools had their own area of focus and expertise.
The five Great Schools were the Bene Gesserit Sisterhood, the order of mentats, the Swordmasters of Ginaz, the Suk Doctor Inner School, and the Spacing Guild. Each of the schools had their own agenda in dealing with humanity, and each had their own specialty in helping human-kind.
After the transfer of power to House Atreides, each school continued to flourish or decline in their own respective areas. Mentats, for example, were banned under Leto Atreides II, but the study of medicine under Suk doctors were allowed to grow.