Exactly what it says on the tin. What if the US, rather than actually putting men on the moon, tried to fake the lunar landings, only for their ruse to be busted by the Soviets? I imagine, at the very least, that America's pride and its faith in the soundness of its scientific institutions would've taken a very stinging blow.
The idea for this topic comes from a criticism I read of the "moon landing hoax" conspiracy theory; i.e. no amount of NASA fakery would've been able to fool the Soviets, and even the slightest evidence that it wasn't absolutely real would've been pounced on and used to turn America and NASA into laughingstocks.