Henry Jackson was born in 1839, the son of an eminent Sheffield surgeon of the same name. He attended Sheffield Collegiate School and Cheltenham College before entering Trinity College Cambridge in 1858. He graduated BA in 1862 as third Classic. He was elected a Fellow of Trinity in 1864 and became Assistant Tutor in 1866, Praelector in Ancient Philosophy in 1875 and Vice-Master in 1914. In 1906 he succeeded R. C. Jebb as Regius Professor of Greek. Jackson was a great reformer, both within the college and the university. Together with Henry Sidgwick and others he essentially established the Cambridge supervisory system by introducing it in the classical side at Trinity. Other disciplines and other colleges soon followed suit.
Jackson's area of study was Greek philosophy, but he did not publish greatly - editing book 5 of Aristotle's Nicomachean Ethics and writing a series of pieces on Plato's later theory of ideas in the Journal of Philology. His greater achievement was in his lectures and his ability to train the next generation of classical scholars; his more eminent students included R. K. Gaye, Francis Cornford and R. G. Bury. He died in 1921.