The term "medieval" comes from the Latin meaning "middle age." The term medieval (originally spelled mediaeval) wasn't introduced into English until the 19th century, a time when there was heightened interest in the art, history and though of the Middle Ages.
There is some disagreement about when the Medieval Period started, whether it began in the 3rd, 4th, or 5th century AD. Most scholars associate the beginning of the period with the collapse of the Roman empire, which began in 410 AD. Scholars similarly disagree about when the period ends, whether they place the end at the start of the 15th century (with the rise of the Renaissance Period), or in 1453 (when Turkish forces captured Constantinople).
Much of the early literature of this period consists of sermons, prayers, lives of saints, and homilies. Somewhat later than the religious writers, the English secular poets appear. The figure of King Arthur, an ancient British hero, attracted the attention (and imagination) of these early writers. Arthur first appeared in literature in the Latin "History of the British Kings" (around 1147).
From this period, we see works like "Sir Gawain and the Green Knight" (c.1350-1400) and "The Pearl" (c.1370) both written by anonymous authors (perhaps the same author?). We also see the works of Geoffrey Chaucer: "The Book of the Duchess" (1369), "The Parliament of Fowls" (1377-1382), "The House of Fame" (1379-1384), "Troilus and Criseyde" (1382-1385), the very famous "Canterbury Tales" (1387-1400), "The Legend of Good Women" (1384-1386), and "The Complaint of Chaucer to His Empty Purse" (1399).