A rolling stone gathers no MOSS. The meaning is obvious.

A rolling stone gathers no moss is an old proverb, credited to Publius Syrus, who in his Sententiae states, People who are always moving, with no roots in one place, avoid responsibilities and cares. As such, the proverb is often interpreted as referring to figurative nomads who avoid taking on responsibilities or cultivating or advancing their own knowledge, experience, or culture. Another interpretation equates "moss" to "stagnation"; as such the proverb can also refer to those who keep moving as never lacking for fresh ideas or creativity.[ Wikipedia]

It means people who are on the move ( rolling stones) will end up having no specific roots anywhere ( they gather no moss ) and that this the downside of it. It has also another meaning ,that when people keep moving from place to another ,they avoid by that picking up responsibilites or cares.