The "ghost" that haunts the characters in this play is Captain Alving. Even though he is dead and his ghost never literally appears during the play, his memory and his actions when he was living drive the plot.
As the play opens, the Captain's widow is building an orphanage in his memory. She's not doing it out of love, however. Alving was a degenerate, in her words. He had many affairs, and they had been separated for many years. Their son, Oswald, returns home for the dedication ceremony and tells his mother that he is dying from some sort of inherited disease. She tells him about his father and says that the disease must have come from him. The word "syphillis" is never used in the play, but we can't help concluding that it is the disease. That's not the end of the Captain's influence, though. Oswald falls in love with his mother's maid, Regina, and wants her to help him commit suicide. Mrs. Alving is forced to reveal that Regina is really Oswald's half-sister. The Captain had had an affair with her mother.
The sins of this father were certainly visited upon his children!