Wikipedia describes a Knight-Errant as being:

A figure of medieval chivalric romance literature. The adjective errant (meaning "wandering, roving") indicates how the knight-errant would wander the land in search of adventures to prove his chivalric virtues, either in knightly duels (pas d'armes) or in some other pursuit of courtly love.

The template of the knight-errant are the heroes of the Round Table of the Arthurian cycle such as Gawain, Lancelot and Perceval. The quest par excellance in pursuit of which these knights wander the lands is the Holy Grail. The genre developed under the patronage of Eleanor of Aquitaine and her daughter Marie of France is the knight-errant Perceval, the Story of the Grail written by Chrétien de Troyes in the 1180s. Although the character is part of the romance genre as it develops in the late 12th century, the term "knight-errant" itself is younger, for the first time recorded (as knygt erraunt) in the 14th-century poem Sir Gawain and the Green Knight. Knight-errantry tales remain popular with courtly audiences throughout the Late Middle Ages. They are written in Middle French, in Middle English and in Middle German. In the 16th century, the genre becomes highly popular in the Iberian Peninsula, Amadis de Gaula was one of the most successful knight-errantry tales of this period. In Don Quixote (1605), Cervantes satirizes the Amadis romans and their popularity. Tales of knight-errantry then fall out of fashion for two centuries, until they re-emerge in the form of the historical novel in Romanticism.