Anglo-Saxon is a term used to describe the people who lived in the south and east of the British Isles from the mid-5th century AD to the Norman Conquest of 1066 that took place after the Battle of Hastings. They were originally Germanic tribes—the Angles, the Saxons and the Jutes (and possibly a small number of Franks and Frisians)--who gradually conquered England and part of what is now Scotland after much raiding, and ruled it until the Norman Conquest. They were heathen at first (e.g. most of the days of the week were named after their gods), but were converted to Christianity, mainly in the 7th century. They spoke Old English (actually a variety of dialects), from which Modern English is descended.
Anglo-Saxon is still used to refer to the people in and originating from England, and is used (especially by the French) to mean the U.S. and Britain acting in combination, as in "Anglo-Saxon diplomacy".