They are celebrating a special occasion, the marriage that is soon to come of Sheila and Gerald. They all seem to like alcohol especially Eric who we find out later in the play is an alcoholic, it transformed him from being a responsible adult to a reckless man. The inspector then rises speculation that Eric when under the influence raped Eva Smith, so the whole concept of them drinking endlessly in celebration is ironic.
The main reason that Arthur is so happy about his daughters marriage is that when they are united it will create a big business partnership because Gerald's father has a knighthood he thinks he will be able to raise higher on the social scale with this relationship. I feel after watching Arthur I would describe him as a sicophant. He is always kissing up to people higher and richer than him, boasting that he is becoming friends with Sir Croft.
Birling assumes that in the near future the Birlings and the Crofts can join together, his reason for hoping this is to make " lower costs and higher prices" he also thinks that there will be no war and that the Titanic is "unsinkable". He foresees great things for him when he couldn't be more wrong.
I think he is a hypocrite, he is only out for himself, trying to avoid the inevitable. Birling rejects the idea of community " But the way some of these cranks talk and write now, you'd think everybody has to look after everybody else, as if we all mixed up together like bees in a hive - community and all that nonsense". This is his outlook on life, that a man should look out for himself. The doorbell rings when it does because everything Birling has just said about looking after yourself, is contradicted by the inspector. He has totally made the audience look at a different perspective, they now see and understand that all Mr Birling has said is proved to be wrong. The door bell has great significance in the sense that it proves that there is something else to Arthur.