16, 24 and 32-bit colour...

 

16-bit colour (High colour, from back in the day), can display 65,536 colours, which is fine for most uses.

24-bit colour (True colour), can display 16,777,215 different colours.

32-bit colour, also supports 16,777,215 colours but also has an alpha channel and using the alpha channel can create gradients, shadows, and transparencies.

To explain the alpha channel? In 32-bit graphics systems there are four 8-bit colour channels, three 8-bit channels for red, green, and blue (RGB) and one 8-bit alpha channel. The alpha channel is a mask not a colour. The alpha channel specifies how the pixels colours should be merged with the next pixel when the two are overlaid, one on top of the other.

Can my eyes tell a difference?

Most users can't. But custom programs that use gradients, shadows, transparency, etc. you may notice a difference with 32-bit colour.