Skeetendo

A palette (at least in Gameboy/Color terms) is a set of four colours (for Gameboy Advance, palettes contain 16 colours). Two of the colours are often white and black (although they don't have to be), and then two colours that can be anything.

A colour in a Gameboy/Color game is stored in two bytes. Remember, a byte is 8 bits. So two bytes means 16 bits.

A colour is really a combination of intensities of red, green, and blue. Each intensity (red/green/blue) uses 5 bits.

So the 16 bits of a colour look like this:
0 RRRRR GGGGG BBBBB

Notice that the left-most bit is always 0. It is unused because only 15 of the bits are used to define the colour (5 * 3).

And these 16 bits are only the data for one colour. So there will be multiple sets of 16 bits to make different colours in a palette.