When you have one bit for every pixel, this pixel can be black (=no light) or white (=light) on your monitor. When you have 8 bits, this same pixel can have 256 diffent intensities of light. These are numbered 0 for black to 255 for pure white.
On a black and white monitor, or monitor setting, you get 256 greyscale values.
A colour monitor works with three different colours to build up light, and every colour can be set to 256 different intensities. These colours are Red, Green and Blue (RGB). The specific value of each colour is added to the result colour. So if all three of the "channels", because that is how they are called, are at full power, you get white light. And if red and blue are off (at zero) you get green at the intensity it is set.

The same for printing, only there the colour has to be printed with a mixture of small dots from the screening. The colours that are mostly used are Cyan, Yellow, Magenta. In the ideal circumstances, you should be able to make all colours with these, but because of the imperfection of the pigments, you need to add Black ink to get a (unfortunately still) washed out view of what you see on your monitor.

Sometimes in print, when you need really specific colours that can't be mixed, you need to add what is called a spot colour. This information is stored in yet another channel that is called "Spot Channel".

You can also make masks to cover up some areas that you don't want to include or work with. These are saved as selections in yet another channel called "Alpha Channel". This makes some parts transparant, and some opaque.