From Bulbapedia, the community-driven Pokémon encyclopedia.
The mayor of Diglett Village (Japanese: 村長 Village Headman) is a minor character who appeared in Plant It Now... Diglett Later.
The mayor tried to stop the Diglett thieves from taking the Diglett. Ash and his friends helped the mayor prepare to defend against the thieves, but then they discovered the real reason behind the thieves stealing the Diglett every year. It turned out that they were really residents of Diglett Village who wanted to check on their parents and make sure they stayed fit. Ash and his friends then agreed on helping the "thieves".
After the elderly Diglett Village residents thought they had driven away or captured all the thieves, the mayor gave Ash and his friends a Silver Wing Badge for their efforts in helping. They were happy to get the badge and wondered if it was related to the silver Pokémon they saw earlier.