What was the cultural impact of the invention of the radio?

The previous answer does a great job of talking about the cultural impacts of radio that are more economic and political.  I'd like to add one other impact.

The beginning of commercial radio is associated with the 1920s, which was a time of great cultural upheaval in the US.  Along with other media, such as movies, and other technology, such as cars, the radio helped bring in a new era in which Americans had many more entertainment options.  This led, historians say, to a new culture whose nature is captured in the terms "Roaring '20s" and "Jazz Age."

This new culture was typified by the flappers and their new, more hedonistic values.  The new culture inspired backlashes as well, such as the rise of religious fundamentalism and of the KKK (which at that point was more focused on nativism and anti-newness than it was anti-black).

The radio didn't do this stuff all by itself, but it was an important factor.