This is called a Quine.
So let's see what main() does:
printf(s,34,s,34);
34 is the ASCII code for the character " (double quote), so this is the same as:
printf(s, '"', s, '"');
The first argument to printf(3) is the format string. The string passed is:
"char *s = %c%s%c; main(){printf(s,34,s,34);}"
So, printf(3) will output exactly that, but note the %c, %s and %c format specifiers, which instruct printf(3) to print a character, followed by a string, followed by another character in that place, which are respectively the 2nd, 3rd and 4th arguments.
The characters, as we saw, are both ", and the string is s again (the same string). So the program output is:
char *s = "X"; main(){printf(s,34,s,34);}
Where X is the string s in the program. So we get this as output:
char *s = "char *s = %c%s%c; main(){printf(s,34,s,34);}"; main(){printf(s,34,s,34);}
Which, interestingly, is the program source itself.