The dragon boat festival has been associated most frequently with the action of Qu Yuan, a poet and a minister in one of the seven warring states prior to the unification of China by the Qin (late in the third century B.C.). Qu Yuan had opposed a proposed merger of his home state with Qin and when he was dismissed, committed suicide by jumping into the river. It is said that the people of his state tried to save his body for proper burial by roiling the water of the river to distract the fish from feeding on it. Another servant of this state, Wu Zixu, is also said to have died on the same date, thus strengthening tradition regarding the celebration. Indeed, a third death on this date is said to have contributed as well. Cao E, a young woman's whose father had fallen into the river, searched for his body until both were found several days later, an act of filial piety by a daughter. The first two deaths were recorded in Sima Qian's classic history as both exemplified loyalty, a Confucian virtue (though their causes were hopeless).
[More recently, the festival achieved the status of a Google doodle.]
Many other folk beliefs have contributed to this early summer event. These have contributed folklore regarding luck to be earned by balancing an egg on its end and defense against illness by wearing herbs in pouches. Realgar wine was valued for its power to ward off evil as well as disease. It is probably an acquired taste.
Many Chinese folktales include references to this festival including the Legend of the White Snake, said to be one of the "China's Four Great Folk Tales." This folktale has several forms, briefly summarized in a Wikipedia article linked. The story has been brought to American theater most notably by Mary Zimmerman in New York City in 2013, see review in the New York Times, linked.
It would be a shame not to mention that the Dragon Boat Festival is a special occasion - as if one is needed - for special dumplings (glutinous rice with sweet and savory fillings, see image picked at random from very many on the Internet).