The 'M' symbol stands for Manual mode (fully manual). In this mode you have full control of your camera. You decide what aperture and shutter speed to use in order take a correctly exposed image. In this mode you can also override any of the camera settings, i.e. flash, ISO, exposure compensation and white balance.
Choose this mode if you are fully confident about how the aperture and shutter work together to produce a correctly exposed image. I use this mode mostly for landscape, close-up portraits, snow and night photography, and even just experimenting with different exposures.