In An Inspector Calls, what is the significance of inspector Goole ?

Inspector Goole, as his name implies, represents the unnatural or spiritual. The name is a play on the word 'ghoul' which is an evil spirit or a phantom. Furthermore, the word can also refer to a person who has an unnaturally morbid fascination with death or disaster.

The inspector fits both descriptions, since his arrival and departure are both quite surreal because he leaves just as mysteriously as he comes - he literally disappears into thin air. Added to that, he has an uncanny knowledge of all the characters and he shows a fixation with the deceased Eva Smith and repeatedly mentions the circumstances and conditions of her demise. A normal person would not focus so much on the finer detail. The inspector, though, almost seems to relish talking about Eva's death, as illustrated in the following extracts:

Two hours ago a young woman died in the Infirmary. She'd been taken there this afternoon because she'd swallowed a lot of strong disinfectant. Burnt her inside out, of course.

When I was in the Infirmary looking at what was left of Eva Smith.

That was what I asked myself tonight as I was looking at that dead girl.

A girl died tonight. A pretty lively sort of girl, who never did anybody any harm. But she died in misery and agony - hating life -

Yes, she's dead.

We soon realize that inspector Goole's purpose is to remind the Birlings, as well as Gerald Croft, that they are responsible for other's destiny. They hold the lives of others in their hands and should, therefore, be more responsible. Furthermore, he makes it clear that none of his audience can be absolved:

This girl killed herself - and died a horrible death. But each of you helped to kill her. Remember that. Never forget it.

He wants to make it pertinently obvious that each one had a role to play in the unfortunate girls' suicide. In each instance, each one was culpable in driving her closer to the edge. The inspector wishes that they would all accept what they had done and not forget it. 

Inspector Birling is a symbol for humanity's moral conscience. It is our conscience that makes us judges of our own character. Our integrity is based on the level of responsibility we acknowledge for our role in what happens to others. Inspector Goole came not only to remind his immediate audience but also those of us who watch or read the play. We should be guided by a moral compass that reminds us of the evil of prejudice and arrogance. Since his listeners in this regard were careless, manipulative and abusive because they thought themselves better than Eva Smith, they destroyed her.

This, ultimately, is the lesson that we must all learn: We are responsible for what happens to others if we have the power to manipulate and affect their lives and, we must acknowledge our culpability and our guilt if our actions result in a tragic outcome for those who had become our victims. The inspector came to remind us all of that.