In medieval England, a reeve was someone who managed the estate of a lord, balancing its books and making sure its operations ran smoothly. In the General Prologue, Chaucer tells us that the reeve on this pilgrimage earns incredible profits for his lord, mainly by being extremely vigilant to make sure that none of the businessmen with whom he works are cheating him. Who were these businessmen, and how might they cheat a reeve?
Well, one businessman with whom a reeve might have worked was a miller, a person who ground corn and grain into flour. A miller could cheat his customers by giving them less flour than they paid for, sometimes by "padding" their sacks with a less expensive substance. Our Reeve, however, is an expert in avoiding this sort of trickery: there's no one with whom he does business, says Chaucer, whose "sleighte and his covyne" (tricks and treachery) the Reeve doesn't catch (General Prologue.606).
The Reeve's obsession with avoiding trickery might have something to do with why he tells a story about two students who try to prevent a miller from cheating them. The subject of this story, then, is one way in which this is definitively a reeve's tale. However, in the General Prologue, we also learned that the Reeve was once a carpenter. When the Miller tells a story making fun of a rather dense carpenter named John, the Reeve takes this as an insult upon all carpenters, and begs to be allowed to "quite," or answer, "The Miller's Tale" with his own. So this tale is also definitively "The Reeve's Tale" in the ways it punishes a fictional miller as a way of answering the "real" one.