The Move-Relearner is a blue-skinned NPC found inside Cerulean City's Pokécenter. He can re-teach your Pokemon moves they have learned before. This can be useful for creating ideal movesets.
Can now be used for free. There used to be a 10,000 Pokédollar fee for each individual move re-learned from the Move Relearner. For instance, teaching 4 moves would cost 40,000 Pokédollars altogether.
The Move Relearner's appearance was most likely based on Bebee2, a distinguished developer of Project: Pokemon.