What are special bicentennial quarters?

Bicentennial quarters are quarters dual-dated 1776-1976, they were produced by the US mint in both 1975 and 1976 (coins for both years are dated 1776-1976). There are also bicentennial half dollars and dollar coins.

The reverse of the quarter features a drummer in colonial dress.

There were over a billion of the bicentennial quarters minted and so they are not rare. All coins intended for circulation are only worth 25 cents, even in Excellent condition. However, some coins were made for sale to collectors, these have "S" mintmarks and are generally found in mint packaging. These are worth more than face value with the ones minted in 40% silver worth more than the ones in the common copper-nickel clad. If your coin does not have an "S" mintmark, it is only worth 25 cents.