A person that is always on the go, and it doesn,t mean that they are always doing something productive,they just have to be on the move. There are times when they finish one thing and move on to the next. Sometimes these folks are productive. A workaholic could be linked to this pharse.  

 "a Rolling Stone Gathers No Moss "

it means that people who are always moving, with no roots and are always trying to avoid responsibilities, at the end, they have nothing in their hand.

So it is better to stick to one thing, realize your responsibilities and work hard in order to get reward at the end.

 Wow, I guess I'd missed all the negative connotations to this.  I thought it just meant that one kept moving forward, and didn't get stuck in a rut. A moss covered stone tends to get cemented in place, over time.  In our family, we have converted it to "A closed mouth gathers no foot", which is a very positive take.