In 15 bit highcolour, one of the bits of the two bytes is ignored, and the remaining 15 bits are split between the red, green, and blue components of the final colour, like this:
Bit 15 14 13 12 11 10 09 08 07 06 05 04 03 02 01 00 Data x R R R R R G G G G G B B B B B
Each of the RGB components has 5 bits associated, giving 32 intensities of each hue. This allows 32768 possible colours for each pixel.
When all 16 bits are used, one of the hues (usually green) gets an extra bit, allowing a 64 levels of intensity for that hue, and a total of 65536 available colours.
Unlike Planar or Chunky graphics, there is no need for a colour look-up table (CLUT, or palette), because there are enough available colours per pixel to represent graphics and photos reasonably satisfactorily.
See also: Planar, Chunky, Truecolour