The main case for this function is when s is not NULL and wc is not L'0'. In this case, the wcrtomb function converts the wide character wc to its multibyte representation and stores it at the beginning of the character array pointed to by s. It updates the shift state *ps, and returns the length of said multibyte representation, i.e. the number of bytes written at s.
A different case is when s is not NULL but wc is L'0'. In this case the wcrtomb function stores at the character array pointed to by s the shift sequence needed to bring *ps back to the initial state, followed by a '0' byte. It updates the shift state *ps (i.e. brings it into the initial state), and returns the length of the shift sequence plus one, i.e. the number of bytes written at s.
A third case is when s is NULL. In this case wc is ignored, and the function effectively returns wcrtomb(buf,L'0',ps) where buf is an internal anonymous buffer.
The behaviour of wcrtomb depends on the LC_CTYPE category of the current locale.