What is the meaning of a thick, dense sock, and the possibility of continuing to walk, and how sound is the argument based on Al-Nawawi's statement regarding the permissibility of wiping over thin socks?

A thick khuff (leather sock) is one that covers the foot, so that nothing of it is visible, and it can be walked in during travel and at home. It is not a condition that it must be possible to walk long distances in it. It is permissible to wipe over a thin sock, even if it shows the skin, due to the generality of the evidence and to make things easy for people. This is the most correct opinion.