If you happen to have access to the relevant movie -- Arceus and the Jewel of Life -- they do a pretty good job explaining it. I'll try to recreate it.
The bottom line is that it is directly related to the Type Plates. In the movie, Arceus is always seen with a series of flat tablet shape objects, forming a ring around him around his golden ring section of his body. Each of these Plates is imbued with the essence of the Type it corresponds to. These are the same Plates we find in the games -- Flame Plate, Splash Plate, etc.
For regular Pokemon, these Plates are hold items, that increase the damage of the holder's moves matching the Type of the Plate. In the movie, Arceus used these Plates to alter his capabilities. As an example, he would use the Mind Plate (Psychic Type) to negate an incoming attack that was of the Psychic type. He could then activate the Dread Plate to launch a devastating counter attack.
When he's not channeling the essence of one of his Plates, however, he's more or less a blank slate. This matches up pretty well with the Normal type. If you check the type effectiveness, the Normal type is very well rounded. It is not Super Effective against anything. It's only weakness is Fighting type. It is only "not very effective" against Steel and Rock. And Normal and Ghost are mutually "no effect" in most situations. It has the same kind of generalist applications that movie Arceus has.
It is this transformative nature that GameFreak tried to cross over to the game from the movies.