In A Christmas Carol, what was the purpose of the first spirit's appearance?
The first spirit to appear in the novel is Marley's ghost; indeed Stave One of the novel is entitled "Marley's Ghost." Scrooge first sees Marley's face in the door knocker, and then Marley appears as a figure in Scrooge's bedroom. Marley explains to Scrooge that, as a spirit, he is condemned to "wander through the world . . . and witness what it cannot share, but might have shared on earth, and turned to happiness." Dickens has already mentioned that Scrooge and Marley were "of one mind" in life, so when Marley explains that he now carries the chain he "forged in life" through his behaviour, he is warning Scrooge that the same will happen to him if he persists. Marley is explicit in his reasons for speaking to Scrooge, although he notes that he has sat beside him many times before and does not understand why, on this particular occasion, he should be visible. Marley is here "to warn you, that you have yet a chance and hope of escaping my fate."
Marley, effectively, is a herald for the other spirits--he notes that these spirits will visit Scrooge as a result of Marley's "procurement" of them. He also explains that the spirits' visits are the only way that Scrooge can "hope to shun the path [Marley] treads" in his "fettered" death.
The first of the three spirits Marley describes, the Ghost of Christmas Past, duly appears to Scrooge as Marley said, to remind Scrooge of his own past as the first step on his journey to redemption.
I’m unsure whether you are referring to Marley's ghost or the Ghost of Christmas Past so I’ll give you an answer for both. Marley’s ghost appears to Scrooge to warn Scrooge that he has been sentenced to walk among the people he avoided in life and to carry the chain that he “forged in life." He warns Scrooge to change the cruelness of his ways, and he warns him that three spirits will visit him over the next three nights.
The Ghost of Christmas Past takes Scrooge on a walk through Christmases past from the time he was a lonely boy to his time as an apprentice with Fezziwig, a kind man, and finally to the time when he loses his love because of his love of power and money. Scrooge begins to realize that this was the point that he began to turn into a bitter man.
By allowing him to become nostalgic, the Ghost of Christmas Past was touching into Scrooge's emotions, things he had long discarded. Scrooge as an adult saw the world as a cold and unhappy place. By allowing him to see times when his world was happy, and when he himself was happy, the spirit is preparing him to see Christmas Present with an optimistic and not cynical attitude. If the Ghost of Christmas Present had appeared to Scrooge with no preparation, he would have likely ignored everything he saw.