There were two different orders of friars known as the Mendicants in the 13th century: the Franciscans and the Dominicans.
The Franciscans were founded by St. Francis of Assisi (c. 1181-1226). Francis, the son of a wealthy merchant, had a life-changing experience when he became convinced that God said to him, “Francis, go and rebuild my house; it is tumbling down”. Francis took this literally and left everything to go off in search of Churches to restore, much to his father’s objection. He became an ascetic, living as a beggar and preaching. He visited Pope Innocent III (c. 1160-1216) in 1210 who was greatly impressed by Francis, and approved the creation of the brotherhood of Assisi. In 1216, the brotherhood took the name the Order of the Friars Minor. The Franciscans lived very humble lives as beggars, preaching and doing good works around their town. St. Clare of Assisi (1194-1253), after being greatly moved by one of Francis’s sermons, established the Second Franciscan Order (the Poor Clares) comprised of nuns, with Francis’s approval. A third order was established for laymen who could not afford to leave everything and become beggars. This order included many people of great stature and historical significance, including King Louis IX, St. Elizabeth of Hungary, and Dante.
The Dominicans were named for St. Dominic (1170-1221), a contemporary with St. Francis of Assisi. The Dominican Order was founded as a response to the Albigensian heresy, which was drawing away Catholics with its extremely ascetic views. Dominic wanted to show that the Catholics could live ascetic lives as well, and all clergy weren’t necessarily worldly and wealthy, as some people (including the Albigensians) assumed. The Order of Friars Preachers, as it called itself, was ratified by Pope Honorius III (1150-1227) in 1216 and 1217. The Dominicans focused much more of their attention on learning than the Franciscans, who did not regard learning as important at all.
Both the Franciscan and Dominican orders had great influence, and they both persist to this day.