Crucifixion has become a formative concept in Christian theology but doesn't feature highly in most contemporary Christian discussion. So what are we missing out on? Let me suggest just two ideas.
From the artistic representations of crucifixion available we see that it's a humiliating way to die. Sometimes the victim had been beaten beforehand. Sometimes the victim was naked. Total exposure to the elements and to the world. In the cross of Christ we see humiliation and scorn in the eyes of the world. There is no glory here, none that looks like pomp, celebration or adulation. If this is how Christ was willing to die, Christians are compelled by their obedience to be willing to be subject to humiliation for following him.
Beautifully, this spares us from being worried about blasphemy. If Christ was willing to be humiliated on the cross, there are no signifiers strong enough to turn him away. The world can continue to profane his name but we have no right to be offended by that. Jesus is willing to bear the brunt of it.
Abandonment of Power
Jesus died as a political enemy of Rome, through the same method used to execute terrorists and revolutionaries. He refused a crown from his followers. He rode into Jerusalem on a donkey, evoking the image of the conquering Davidic king. He refused to call legions to fight for him. He refused all the trappings of a political messiah of the type of the Maccabees or the Judges. And yet he died the death that Rome would have ordered for any of these.
To be crucified along with Jesus is to die a similar death; a death that abandons all the power structures of this world. It's a death that faces Caesar and refuses to become Caesar. To die to that death is to be free from that kind of politics, and be free to engage in the politics of loving the neighbour. The political power of the church is not found in lobby groups or petitions. The power at our disposal is the power to freely act, to be indifferent to Caesar in the act of loving the neighbour. This is the real, social and political power of the church.
Crucifixion as a theological concept formative for the Christian subject opens us to thinking about living in ways separate to the ways of the world. If we are truly crucified with Christ, we share in that death in many ways. Sharing in that death then allows us to live as Christ, free from the constraints of Rome.