The big expression in the middle is effectively unpacking a 2D point encoded in z. z % 9 is the x coordinate and z / 9 is the y coordinate:

  x = z % 9;
  y = z / 9;

  putchar (
          x + y > 3 &&
          x + y < 14 &&
          y < x + 6 &&
          y > x - 5 ? '*' : ' ' );

  if (x == 8)
    putchar ( '\n' );

Wolfram Alpha plots this inequality nicely:

http://www.wolframalpha.com/input/?i=x+%2B+y+%3E+3+%26%26+x+...

The program is drawing on a grid 9 wide by 10 high. The loop is going over each space in this grid. It puts a * in each cell that falls within the equations described by the four inequalities. Here's a slightly more simplified version.

    int putchar ( int ) ;
    
    int main ( void )
    {
        int z;
        int width = 9;
        int height = 10;
    
        for (z = 0; z < width * height; z++)
        {
            int x = z % width;
            int y = z / width;
    
            putchar (
                x + y > 3 &&   /* top left */
                x + y < 14 &&  /* bottom right */
                y < x + 6 &&   /* bottom left */
                y > x - 5      /* top right */
                 ? '*' : ' ' );
    
            if (x == width - 1)
                putchar ( '\n' );
        };
        putchar ( '\n' ) ;
    
        return 0;
    }

It would be clearer to separate the main loop into nested loops for x and y, but I've left it as is to show a closer resemblance to the previous version.

The fun part is that you can now play with the various settings. Try increasing the height and width and scaling the equations appropriately. Replace x by 2 * x or x * x for more interesting shapes. You can bound the picture by any equations you like. Example: http://ideone.com/53Qh3