Symbolism, Imagery, Allegory
The House of the Interpreter is sort of like school for Christian. "The Interpreter" who lives there takes him from room to room, showing the new pilgrim images representing Christian principles. You can also think of it as your own training ground for reading the allegories of the story as a whole. The Interpreter tells Christian before he leaves to "keep all these things in thy mind, that they may be as a goad in thy sides, to prick thee forward in the way thou must go" (P177).
Mmm. That sounds pleasant. Christian is like a horse, and these images are like spurs.
You can almost imagine Bunyan saying the same thing to you as a reader. Like the allegories of the novel, the allegories of the Interpreter are active. In other words, rather than static or ambiguous symbols of "innocence" or "wisdom," they represent complex states of being.
This is particularly poignant and meaningful in the case of the caged man, who tells Christian:
"I am what I was not once… I am now a man of despair, and am shut up in it, as in this iron cage. I cannot get out, O now I cannot." (P158)
Oh my.
Simply seeing the image of a man in a cage is not enough to make Christian understand the nature of despair. Instead, he has to question him to understand that God (who Christian reminds him is all-forgiving) has not locked the man up, but that, as he says "I have so hardened my heart that I cannot repent" (P160). Basically, if the caged man could just repent, he'd be set free.
The way Christian interprets the things he is shown (with the help of the Interpreter) is a model for how we can interpret the allegories of The Pilgrim's Progress. This could also be an good moment to look back at the Apology, where Bunyan defends his use of allegory as a style. How do the Interpreter's words seem to support Bunyan's argument about teaching through images?