Take a look at the following bit layout above. We can see that there are 16 bits here or 2 bytes. The Gameboy Advance uses 2 bytes to store color information. However, out of those 16 bits it really only uses 15 bits. That's why the last bit you see has an x, that bit is never used and is always 0. The reason it isn't used is because the Gameboy Advance stores colors in RGB format where each color channel uses 5 bits. So you use 5 bits for red, 5 bits for green, and 5 bits for blue. Which bits correspond to which color is shown in the diagram.
This means that each color channel can have 32 different values (0-31) since 25 = 32. Also, since we only use 15 bits to represent a color, we can only have 215 = 32,768 colors represented on the Gameboy Advance. Like I said before, not a ton of colors, but good enough.
Below is a color calculator you can use to find the hexidecimal for any color you want to display on the GBA. This calculator is fairly simple, you just choose the color you want from the color picker and see the corresponding color that would appear on the GBA. Because the colors you choose from the color picker have r, g, b ranges from 0-255, we have to convert that range to be between 0-31 first, so different colors in the color picker can result in the same color on the GBA.