This phrase sounds paradoxical, like it could not possibly be true, but it is good advice in many situations.
I have found the phrase is easier to work with if you use another version of it. Military special forces have a phrasing, "Slow is smooth. Smooth is fast." If you can work smoothly, the work tends to go faster. If you watch an expert at a job that involves working with one's hands (gardener, blacksmith, potter), their movements are always smooth. By being smooth, they don't have to waste as much time correcting mistakes. The best way to be smooth is to take it slow and not rush yourself.
Those mistakes also add up very quickly in space, so the phrase is even more important up there. It reminds me of another quote, this one by Chris Hatfeld, who was one of the astronauts who worked onboard the real ISS:
Astronauts have a saying, "In space, there is no problem so bad that you cannot make it worse."
I think he'd be a big fan of moving smoothly.