A rough road is a road that has bumps, cracks, is uneven etc.
Rough roads are those that need work on them to smooth them out and when you drive on the rough road your car may experience vibrations, shaking etc.
Most rough roads will eventually get repaved to smooth them out if there is enough money eventually to repave them.
Thankfully we had a rough road repaved last month which was a 11 mile stretch that goes from a town I work in to the town I live in.
That road used to be really rough that it would shake my coffee cup around in my cup holder and sometimes spill my coffee.
Now it's been repaved and is much smoother.