Middle English (c. 1150-1500): It's the language spoken/written between Old English and Early Modern English (Elizabeth's and Shakespeare's English)
Old English did not "die out" so much as it was overthrown in battle and subjugated by Norman French after the Battle of Hastings in 1066. William of Normandy's barons became the rulers of many Anglo Saxon communities, and their courts spoke Norman French, though "literacy" continued to be associated mainly with Latin. (The term "literatus" specifically meant someone was "Latin literate" and there was no term for Anglo-Saxon literacy.) However, some nationalistic Normans began recording histories and romances and lyrics in Norman French, sometimes jotting down those quaint old Anglo-Saxon poems in the margins, as well, and in some rare instances (the "Exeter Book") dedicating whole pages or even books to them. However, between about 1150 and 1300, the English ceased to regard Norman French as a standard language of commerce and daily discourse, reserving it for legal pleading (our courts' "Oyez, oyez" asking all to hear the judge's words), legislation, and sophisticated courtly activities like lyric poetry and love talking (which we still call "amorous" behavior). Old English syntax (subject-verb-object) won out over Norman French syntax (object-subject-verb and object-verb-subject), except in poetic usage, where NF syntax is considered "artistic embellishment" (i.e., courtly or privileged syntax). Both Old English and Norman French words began to change their meanings to remove ambiguity about what they named, and typically Middle and Modern English speakers find words rooted in Old English vocabulary sound more "simple" or "direct," whereas those derived from Norman French sound "sophisticated" or "artful." For an early example, see Pandarus' "writing lesson" in Chaucer's Troilus. Sometimes these vocabulary conventions derive from commoner vs. noble uses of the same object (famously, OE "cu" [cow] names the animal in the field and Anglo Norman "boef" [beef] names the meat on the table). Because Old English filtered up through Norman French, OE dialects were largely preserved in Middle English. Northumbrian speakers had a hard time making themselves understood by speakers of "East Midlands" around London (i.e., East Saxon + Jutish dialect), and "Westron" men from near the Welsh border (West Midlands) sounded quaintly old fashioned to the cosmopolitan East Midlands speakers. "Southron" men, from nearer the Cornish border, also sounded exotic to those at the center of government and trade. Between 1300 and 1500, East Midlands dialect grew into the Early Modern English that became the dominant sound, and spelling, of educated vernacular English authors like Wyatt, Sidney, Shakespeare, and Queen Elizabeth I. Since most printers and theaters were in the East Midlands, its dialect also became the one we associate with most "English Literature."