It means signals can only propagate about 6 centimeters during a single CPU clock cycle. That makes accessing information off-chip difficult in a single cycle, since 6 centimeters is on the same order as the linear scale of most motherboards.

This limit doesn't immediately impact computations that are carried out entirely on-chip. I expect that's the great majority of computations on today's CPUs, which typically have large caches. So I'm not sure the GP's explanation is correct, although it's certainly interesting.

As an explanation for why you cant get clock speed increases of the same order of magnitude as you could previously, without changing the entire technology, it would seem correct.

6cm now means that you only need to double twice to get to less than the die width.

Also, electricity does not propagate through copper at c, but at between 40% and 90% of it, depending on the inductance and capacitance of the circuit, so you are looking at even less of an increase before you start running into some really thorny problems as not only are you running up against relativistic limitations, but different bits of your chip can be doing it at noticeably different times.

Nothing can't travel faster than the speed of light – including Electric current. So in a hypothetic 5 gigahertz CPU, there couldn't be a path through the wires/transistors longer than 5.99584916 – otherwise, the end result couldn't be correctly determined. That's why CPU's got smaller and smaller. But since the transistor shrinking slows down, and Adders/Multiplyer/Register/Decoding Logic etc. all takes some time and length, it's harder to make a CPU with a shorter longest path.