To canter is ride a horse faster than a trot and slower than a gallup.
Cantering involves three hoof-beats, followed by a rest.
Trotting is a "one-two" beat of the hoofs and galluping involves a "one-two-three-four" motion.

The word canter comes from the English city of Canterbury.
Chaucer's famous book, Canterbury Tales, is about a group of varied people who are on a pilgrimage to Canterbury.
Some of the tales are serious and others comical; however, all are highly accurate in describing the traits and faults of Human nature, Religious malpractice is a major theme as well as focusing on the division of the three estates. Most of the tales are interlinked with similar themes running through them and some are told in retaliation for other tales in the form of an argument.
A pilgrimage is an arduous "road trip" that people go on to a famous religious site. Canterbury was the religious center or church capitol since around 600 and archbishop Thomas Becket was assasinated there in 1170 by knights loyal to King Henry II, after he came into conflict with the king over the freedom of the church from control by the state. Three years later, Becket was canonized by the pope. Henry came down to Becket's tomb and did public penance. Historians believe that Henry never really ordered Becket's death, but only said angry words that the overzealous Knights who's lives ended in infamy.

In summary, the word canter comes from the pilgrimage to Canterbury, the seat of religious power and a place matrydom where a man stood and died for freedom of the church from the state. Pilgrimage is a journey to a significant destination with companions who tell stories to each other and share meals and generally take care of each other along the way.