Dayton is a one-off character from the episode "Takin' it on the Chinchou." He lives with his father Daizou in Blue Lagoon on Blue Point Isle, where the two run the annual Parade of the Chinchou.
The parade itself is pretty central to Dayton's story. His own Chinchou, nicknamed Bright, leads the procession, and when Ash needs to reach the shore, Dayton brings him along. Things go south fast when Team Rocket shows up trying to steal all the Chinchou—their interference destroys the rope bridge that splits the parade in two. Dayton has Bright and the other Chinchou hit Team Rocket with Thunder Wave, and Pikachu finishes them off.
While leading his half of the parade through the mountains, Dayton takes a bad fall down the mountainside. But the Chinchou's antennae let them locate him, so the parade manages to regroup and keep going. The next morning, they finally reach the shore, only for Team Rocket to make another grab for the Chinchou. This time Weezing's Smokescreen throws off Ash's aim, but Dayton gets Bright and the others to use Thunder Wave again, destroying the cage and blasting off the villains for good.
What makes Dayton's arc stick is the bittersweet ending. As the Chinchou prepare to leave for the ocean, Dayton tells Bright goodbye and admits he's looking forward to it coming back someday. After that, Dayton and his father see Ash off to Bluefinland, where Ash catches a ferry to Yellow Rock Isle with his friends.
Content compiled by AnimeList.moe from publicly available sources.