What is the significance of the title, An Inspector Calls, in the context of the play?

The significance of the title is that from the point where
'An Inspector Calls', the lives of each of the characters in the play have changed
forever.

Prior to Inspector Goole's arrival, the Birlings
are having dinner and celebrating their great successes to date and the positive view of
the future for them and those like them. The family are celebrating the engagement of
Sheila Birling, the daughter, to Gerald Croft, son of Lady Croft. Arthur Birling
confides in Gerald that he is likely to be knighted himself. We see as an audience that
Arthur Birling's perceptions are somewhat askew -he dismsses the idea of war, and extols
the virtues of the unsinkable Titanic: both events which had played
out before the drama was performed.

Birling had just been
explaining to Gerald and Eric that one should be independent and not rely on
others.

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BIRLING:...But the way some of these cranks talk
and write now, you'd think everybody has to look after everybody else, as if we were all
mixed up together like bees in a hive - community and all
than nonesense.

It is a
dramatic foil to the socialist message which the inspector delivers to the
family-

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INSPECTOR:...We don't live alone. We are members
of one body. We are responsible for one
another.