It's important to wipe radially, not circularly.
Why is that?
I read that you're less likely to scratch the CD if you rub outward from the center rather than in a circle.
The difference between circular and radial scratches is discussed in
Circular Scratches on CDs and DVDs. Both wipe directions may cause scratches, but the radial ones tend to be easier on the error correction system of the player, hence the advice to wipe discs radially instead of circularly.
