So lets start with a dot or pixel. It is the smallest part of an image that is stored in the computer and is assigned a color. The amount and style of storage of the color depends on how many colors that pixel could have and there are always limits so lets begin with the most restrictive. If the pixel can take only black or white then it needs just 1 bit to store it. That neans that you can have 8 pixels to one byte. So a 1000x1000 pixel image would takes approximately 125 KBytes of storage in RAM (i.e. not too much). At the other extreme is "Full Color" or "True Color" and this can have up to 16 million colors by virtue of the fact that the Red, Green, and Blue channels which make up the color can take any one of 256 shades. That happens to be the number of states in one byte so it takes exactly 3 bytes for an RGB encoded pixel at full color. So a 1000x1000 pixel image in full color takes approximately 3 MBytes (i.e. a lot more).
The R,G,B in an RGB pixel are known as the color channels or components and the number of bits that are required to encode the shade is known as the bit depth. You can have a 24 bit depth image for the 3 channels or sometimes its called 8 bits per component - with the assumed 3 components per pixel.
A grayscale image is universaly known to have one channel and 8 bit depth. The shades within the single channel are luminosity such that a value of 0 is black and a value fo 255 is white ( 0 to 255 inclusive makes the 256 shades ).
Due to the precious nature of memory in computers (especially older ones), there was a requirement to have something in between these two extremes. It would be nice to have images with a few colors on them for graphs, pie charts and other non photographic type diagrams. Where all of the previous type of images used the color bit vale to directly represent the color of the pixel there is another completely different way of doing it and these types of image are known as color index or paletted. They also have a fixed number of bits assigned to each pixel with usually is 4 or 8 but instead of the value being the color, the value is an index into a table of colors where the precise color in the color table can be precisely defined using lots of bits because you only have it defined once per image instead of one per pixel. So now the image has two parts. The color index table or pallete and the pixel information.
By using 4 bits per pixel that gives a range of 16 indexes. So a set of 16 colors are defined in the color table and described each with 24 bit RGB. Windows has a standard set but it is possible to have any colors in that table for a particular custom image.
Much more common tho is to have 8 bits per pixel and a color table or pallette of 256 entries. Often some of them will be made to match the standard windows set which leaves either 240 (or sometimes 236) spare which you can use to define the most common colors in the image to make it with. Usually, having 200 or so colors is enough to turn a full color photograph into one using a third of the memory without losing too much color quality. We will see later why its not usually a good idea to do it tho.
I have implied that the black and white image type is like a direct pixel color type of image but its equally valid to treat it as a 2 shade color index type where it looks up into an implied 2 entry color table. In most painting applications it is treated more like the latter type than former. Very few people use it thesedays in any case because you can do nicer lines using grayscale with antialiasing which will be discussed later.
I think we can finally talk about these images as bit mapped. By this we mean that it has sets of bits mapped to the pixels for the image.
Here are some examples of an image in the following formats. a) Full Color, b) Grayscale, c) Black and White, d) 8 bit color index, e) 4 bit color index (custom palette), f) 4 bit color index (windows palette)