I don't know that they are all friends or anything, but the people at the party are having an argument about the death penalty.  Most of the people there are against it because they think that it is inhumane.  But the host (the banker), argues with them.  He says that it is more humane to kill a person than to lock them up for the rest of their life.

When he says this, the lawyer says that he thinks life imprisonment would be way better than death because any life is better than no life.  That is what starts the bet.  The lawyer ends up betting that he can spend 15 years alone.  If he manages it, he'll get 2 million rubles.