Pedi-Sox are, well, pedicure socks. :) They are open at the toe to let your toes out to be painted. They come in several versions ranging from thick, warm socks to thinner socks for warmer temperatures.
Ravelry: Sassy Pedicure Socks pattern by Lisa Gentry
Ravelry: Pedicure Socks free pattern by Deneen St Amour