A Kappa is a water-dwelling creature. It is humanoid, and resembles a tortoise, save for the bowl-like indentation in its forehead, which is filled with water. Kappa are honourable creatures, but are highly dangerous for wayfarers.
Miyamoto Usagi encountered a Kappa during his wanderings. The Kappa demanded that Usagi pay it a tribute in order to cross its swamp. Fortunately, Usagi had discovered cucumbers growing out of season. As Kappa are fond of cucumbers, Usagi was able to bribe it to let him pass.
Shortly thereafter, Usagi found a house in the swamp, where he stayed briefly. The rabbit learnt that the cucumbers were grown by the old woman who lived in the house to allow her son safe passage to visit her. Usagi returned to the swamp to rescue her son, who was unable to pay the Kappa's toll with the cucumbers gone. Usagi fought the Kappa and forced the water from the bowl in its head, which would spell its death. Usagi exacted a promise from the Kappa never to harm another wayfarer before letting it go.
It was a great surprise to Usagi, however, when he learnt that the samurai he had rescued had ventured this way to visit his mother's grave...
"Kappa" (collected in Book 2: Samurai).