What means ' a ceremony in front of a vicar doesn't make a marriage'?
'...And I wish I had married her!' He turned to Fanny. 'But never mind, darling,' he said, 'in the sight of God you are my wife!'
At these words along, low cry of despair and anger came from Bathsheba’s lips. 'If she’s – that, what – am I?'
'You are nothing to me, nothing,' said Troy heartlessly.' A ceremony in front of a vicar doesn’t make a marriage. I don’t consider myself your husband.'

Here what means 'A ceremony in front of a vicar doesn't make a marriage'?
Does it mean that a marriage is only valid has witnessed by a vicar?

Question

What means ' a ceremony in front of a vicar doesn't make a marriage'?
'...And I wish I had married her!' He turned to Fanny. 'But never mind, darling,' he said, 'in the sight of God you are my wife!'
At these words along, low cry of despair and anger came from Bathsheba’s lips. 'If she’s – that, what – am I?'
'You are nothing to me, nothing,' said Troy heartlessly.' A ceremony in front of a vicar doesn’t make a marriage. I don’t consider myself your husband.'

Here what means 'A ceremony in front of a vicar doesn't make a marriage'?
Does it mean  that a marriage is only valid has witnessed by a vicar?

Answer

Ramona is right. He is hinting that what makes a real marriage is the relationship between the couple, not the participation in some ceremony.

Answer

It means that, to him, even though they were married in a church, in front of a priest, he doesn't consider himself Bathsheba's husband.
I guess he is trying to say that he loved Fanny much more and that is why he considers her his wife, even though they were not legally married.
Far Away from the Madding Crowd, right? :)