The phrase "Post No Bills" refers to many cities' laws which forbid the posting of handbills, or any type of signs on public property. Usually, in small towns and even large cities, the easiest way to get a lost item found or to advertise something (like a garage sale) is to staple signs to the various poles and walls outside where people can see them as they walk by. However, this can damage the poles, and it can make the walls look ugly, and it can detract from the view of the billboards in the area.
Often times, (at least, back in the day) these laws were protested by putting signs all over that said, simply, Post No Bills. This irony failed to amuse city governments, as there were often steeper penalties for these particular signs.
"There's a country's soul that reads 'post no bills'." - 'Calm Like a Bomb', Rage Against the Machine