mid-14c., screne, "upright piece of furniture providing protection from heat of a fire, drafts, etc.," probably from a shortened (Anglo-French? compare Anglo-Latin screna) variant of Old North French escren, Old French escran "fire-screen, tester of a bed" (early 14c.). This is of uncertain origin, though probably from a Germanic source, perhaps from Middle Dutch scherm "screen, cover, shield," or Frankish *skrank "barrier," from Proto-Germanic *skirmjanan(source also of Old High German skirm, skerm "protection," Old Frisian skirma "protect, defend;" from PIE root *sker- (1) "to cut").
The sense of "anything interposed to conceal from view" is by c. 1600. The meaning "net-wire frame used in windows and doors" is recorded from 1859. Meaning "flat vertical surface for reception of projected images" is from 1810, originally in reference to magic lantern shows; later of movies. Transferred sense of "cinema world collectively" is attested from 1914; hence screen test "filmed test of performing abilities" (1918), etc.
The meaning "small fluorescent display on a TV set" is by 1946, extended to the display on a computer monitor by 1970, hence the monitor itself. The computer screen saver is attested by 1990. The meaning "window of an automobile" is by 1904. As a type of maneuver in sports, by 1934 (U.S. football, screen-pass). Screen printing recorded from 1918. Screen-door is from 1840. Screen-time "time spent watching a computer or television screen" is by 1999.