As Megan Garber writes:
In space, however, there is no gravity to pull the dead cells (technically: the detritus) away. Which means that the detritus, left to its own devices, simply floats. Which, given the fact that multiple astronauts live on the Space Station at the same time, and the fact that even highly trained space travelers might get skeeved out by floating clouds of dead skin, is less than ideal.
So as the astronaut says: "This cloud, this explosion of skin particles -- detritus -- floats out. And you're in this weightless environment, and the particles have nowhere to go but out."