How do you make the man blocking cerulean cave to move?

The man who blocks the entrance of the Cerulean Cave in Pokemon Fire Red and Leaf Green is called the Gatekeeper. In order to move him you need to go to Vermilion City and talk to the old man in the house next to the Pokemon Fan Club. He owns the Old Rod, which is a key item that you'll need to progress through the game. Once you show the Gatekeeper the Old Rod he will leave the entrance to the cave and allow you to enter.