How does the S mint mark matter in the value of a Bicentenial quarter?

Because the "S" mintmark means the coin was minted in San Fransisco. Because the coins minted in San Fransisco in 1976 were not intended for circulation, they are more desirable to collectors. Some of the "S" mintmark coins are 40% silver and that boosts their value. If the coin has no mintmark, or any other mintmark other than "S" it has no value beyond face value.