The Giant Step is where the first Melody in Earthbound is located. It is on top of a great mountain, and nobody knows what caused it. The mountain is blocked off until you do a few things at the beginning of the game to get the key.
The Giant Step is located in Onett, the default city of Earthbound. The Area around it is filled with weak monsters, except for two or three. One monster will attack you in groups, but can easily be destroyed with PSI Rockin'. Another monster will leech HP from you, but can easily be defeated. The only monster that you need to worry about is the monster that is guarding the Melody, and the cave to the top of the mountain, the Titanic Ant.
The only people that will ever appear here is Ness. King will never appear, as he doesn't want to go back out after the meteor incident. Paula, Jeff and Poo will not appear while you are here, as they've not been mentioned in the game yet. Though you can come back if you wish.
The vision Ness has here is of a small, cute puppy. The dog was King from his earlier days.