In this speech, Churchill says that the effect of the iron curtain could be the destruction of what he calls “Christian Civilization.”
In this speech, Churchill is saying that the Soviet Union will, if it is allowed to, spread out and conquer as much of the world as it can.  This could happen by invasion or by subversion.  He says that this must not be allowed to happen.  He says that such domination by the Soviet Union would

constitute a growing challenge and peril to Christian civilization.

By saying this, he shows that he believes that the iron curtain, if extended, could have the effect of destroying what he sees as civilization.