Personally, what I think the Mafia means by honor is the rules they basically set out for themselves and if you obey these rules, then you have "Honor". However in this modern world these rules are broken probably everyday and all of them as well. These days for the mob I think honor basically means not breaking Omerta. Although even though that rule is broken from time to time, if you don't break Omerta I think it's fair to say you have some honor. That is because you are not betraying who you are and what you signed up for, your taking your punishment like a man.