These white particles are pieces of the dip tube from your hot water heater. Several brands of hot water heaters were made using a faulty dip tube that disintegrates over time. The dip tube carries the cold water from the top of the hot water heater to the bottom, where the cold water is heated.
Over time, the dip tube disintegrates and the white dip tube particles are carried through the household pipes. If the particles are large enough they are caught in the strainers of the sink faucets or shower heads. If you are experiencing a problem of this nature, call the manufacturer or provider of your hot water heater for further information.