Why does beach has a white or black sand ?

Answer 1

black sand is usually volcanic in its' origin.
White sand is usually coralline in origin.

Most of those lovely white sand beaches we like to roll around on came out the south end of a north bound parrotfish.

Answer 2

I agree with the above answer, but would add that in many places (eg, Australia), beaches often form from the weathering of sedimentary rocks, which produce large quantities of quartz, which produces the white colour. The darker minerals have been weathered away over the millions of years, forming clay which washes away. The less chemically reactive quartz remains.
On volcanic beaches, however, the darker magnesium and iron rich minerals have not yet chemically weathered away, and so give the sand its black colour