It's a multiple play on words, based on the double meaning of "come to dust".
At one level, "come to dust" = "die and be reduced to dust". So it means "Golden lads and girls" (i.e the most worthy people) die just the same as lowly ones like chimney sweepers.
But the joke is that chimney sweepers also literally "come to dust" = "arrive to clean dust (from the chimney)".
Some commentaries also note a third possible meaning (see Google Books http://books.google.co.uk/books?id=ZGpco…
): that "chimney-sweepers" was the dialect name for a plant of the Plantago species whose head eventually disintegrates to dust. The same reference notes that "golden" in Shakespeare is "a term of praise and value", not meaning rich or the like.