As Philip Edwards puts it in his Introduction to The Spanish Tragedy (1959), the supernatural element introduced by the Ghoast of Don Andrea in the Prologue ushers in the theme of revenge. And as Revenge puts it at the end of the Prologue, the Ghoast and Revenge act as the Greek-style Chorus to the tragedy. A Chorus may give important narrative information and describe events that occur off stage. It also may comment upon actions and decisions that occur in the tragedy.
Besides Andrea's Ghoast, other supernatural elements, also present in the Prologue, are various personages of the afterlife, We meet the boatman of death's river, "the flowing streame of Archeon," the "churlish" Charon:
Andrea's Ghoast. Till life to death made passage through my wounds.
When I was slaine, my soule descended straight
To passe the flowing streame of Archeron;
But churlish Charon, only boatman there,
Said that, my rites of buriall not performde,
I might not sit amongst his passengers.
Ere Sol had slept three nights in Thetis lap, (Prologue)
Other keepers of parts of hell are also met: Cerberus; "Sate Minos, Eacus and Rhadamant"; Plutos; the Furies; Ixion; Prosepine; and Revenge. There is some debate between Minos, Eacus, and Rhadamant about which field Andrea should be escorted to: the peaceful fields for lovers or the troubled "martiall fields" for warriors. They call upon Plutos to decide the issue. On his journey to Plutos, a small survey of hell is given him and the reader.
The purpose of this supernatural element is to depict for the reader and to convince the reader of the serious circumstances Andrea faces in his uncertain visit into the upper levels of hell. We know his sojourn in the corridors of hell is uncertain in some regard because (1) they don't know where to put him and (2) Revenge is his guide as they watch Bel-imperia's revenge against Don Balthazar, who is the "author" of Don Andrea's death:
REUENGE. Then know, Andrea, that thou ariu'd
Where thou shalt see the author of thy death,
Don Balthazar, the prince of Portingale,
Depriu'd of life by Bel-imperia:
Heere sit we downe to see the misterie,
And serue for Chorus in this tragedie.
The role of the supernatural has three parts: (1) to develop both the plot and the theme; (2) to depict the seriousness of the circumstances in the tragedy; (3) to provide an objective view of Bel-imperia's attempt to give Andrea revenge.