These are dairy stars awarded by the American Goat Society (AGS).
*D is for a doe that has met the minimum requirements for a dairy star in AGS on either a one-day or another DHI program. You will see numbers in front of the * indicating the # of consecutive generation that doe is in a line of star-doe milkers.
+S/++S are for bucks that have so many different offspring that have earned their dairy stars. You will also see *S or some machination of the two. The * indicates heredity from his dam.
More information is available from AGS.
I was looking for the table the other day but it's not online right now because AGS is revamping their website. (If anyone has the *AGS* table, please let me know, as I only have an old handbook and it's not here with me at the moment.)
ADGA has a similar program, with slightly different requirements. For example, they give awards based on protein, butterfat, and/or milk, while AGS considers only milk and butterfat. ADGA uses *M for their does and *B/+B for their bucks.
So for example, I have a doe named Sandy Hollow SS Butterscotch 3*D 3*M. Until recently, she was a 3*D 2*M, which meant that one of her maternal ancestors did not have a star in ADGA but she did in AGS. That ancestor later earned her star from her progeny and thus it trickled down to all the star does beneath her on the pedigree.