Image modes define the channels that create an image.
Bitmap mode contains one colour, 100% black. The pixels are dithered to create the sahdes of gray. This mode is suitable for printing on dot-matrix printers.
Grayscale mode has 256 colours; black, white and 254 shades of gray. When an colour image is converted to grayscale, all the colours are discarded leaving only brightness values which are converted into pixels. This mode is suitable for printing grayscale images.
Duotone is similar to grayscale but replaces the black with a different colour. This mode is suitable for printing with limited colours.
Index mode contains only a pallet of up to 256 colours. When converting an image to index mode, Photoshop selects 256 colours and replaces the rest of the colours with a similar colour in the pallet. This mode is suitable for web graphics to reduce file size.
CMYK stands for Cyan, Magenta, Yellow and Key. Black is just called key so that it won't be mislead for the colour blue. CMKY mode has four channels, each with their own percentage value to specify the brightness of the channel. This mode is suitable for colour printers. Most printers use the "CMKY" model because inks are subtractive (colours get darker when mixed) and CMY (Cyan, Magenta, Yellow) are more lumious than RGB (Red, Green, Blue).
RGB stands for Red, Green and Blue. RGB mode contains three channels, each with their own percentage value to specify the brightness of the channel. This mode is suitable for screen display. RGB (Red, Green, Blue) are used because light are additive colours (colours get lighter when mixed) and they are darker than CMY (Cyan, Magenta, Yellow).
Lab mode contains 3 channels; lightness, chroma A and chroma B. Chroma A represents 128 colours within a range from green to red, chroma B represents 128 colours within a range from blue to yellow and the lightness represents the lumosity of the image. Lab mode is suitable for editing Photo CD images, transfering photographs and printing on postscript 2 and 3 printers.
Multichannel mode converts channels to grayscale values. Each channel contains 256 colours; black, white and 254 shades of gray. This mode is for specialized printing.