It places a size on the visible universe which is computed by multiplying the age of the universe by the speed of light. If the speed of light were half as large as it is, we would only be able to see galaxies out to about 7 billion light years and not 14 billion. The speed of light also set the scale for how much pressure a gas of 'radiation' produces, and this effects in a big way how rapidly the universe expanded when it was less that 1 million years old. Lower pressure means less expansion and a universe that would be much smaller and denser than it is now.