The Bowser Ghost enemy is a boss in Area 4 and Area 8 (name is really Bowser Spirit). He has a very good likeness of Bowser, but is only a shadow of the real thing.
In Area 4, you find a figure that looks like Mario, but when Luigi gets closer, Bowser takes the place of Mario. And you hear King Boo's voice saying that you must defeat this spirit in order to continue and he also says that he doubts that you would be able to defeat his greatest creation so far. When you defeat the Bowser Spirit, you gain a speical key in the shape of Bowser's claw.
In Area 8, you face the Bowser Ghost again, but not as a final boss of the Area. He has been upgraded to Level 50 and has more powerful attacks than normal. He also gains the ability to summon Koopa Spirits to his aid, much like Bowser can summon Koopas to his aid.
In Area 4 when Bowser's form takes Mario's place, it is like in Area 4 in last game. Bowser's form took Mario's place in the painting he was trapped in.
The Claw-shaped Key you gain in Area 4 if an obvious reference to the only boss in the Mario series that has a good likeness of the Bowser Ghost, Dark Bowser.
The Claw-shaped Key is also a reference to the item that Bowser can use to become Dark Bowser.