How did the phrase "Iron Curtain" reinforce Churchill's overall message in the speech?

Churchill's overall message in his 1946 speech "The Sinews of Peace" is that even though America, Britain and other powerful states have won the Second World War, the world at large still hasn't managed to establish a long-lasting and stable peace. The greatest threats are war and terror.

The phrase "Iron Curtain" invigorates this thesis. It divides Europe into two halves, the democratic West and the Russia-influenced, communist and totalitarian East. This term is extremely rich in associations; the curtain means division which breaks up the post-war prosperity and unity that all the states should strive for. The fact that it is "iron" associates war and destruction, which is why many historians think that this speech marked the beginning of the Cold War.