When applying wudhu you wash/wipe your feet directly with clean water. If you were wearing socks remove them and wipe/wash your feet. NEVER wipe ON the socks.

If you were wearing what Arabs call 'khuf' which are like slippers that cover the whole foot you can wipe on them (All-around not on top) provided that this khuf is made of LEATHER.

Now why do you have to remove the socks but not the leather khuf? Back to logic: Because socks are made of weaved tissue through which dirt can penetrate and reach the feet (like if you step on dirty water). That's why you must remove the socks before you wipe your feet so you can remove any dirt that made its way through the socks material. Whereas the khuf that is made of leather does not allow dirt to penetrate it that's why you only wipe the khuf because your feet are clean, provided that when you put the khuf on your feet were clean.