Try to imagine each track as a glass of say... 10 ml in volume. The moment you hit 0dB, that glass becomes 10 ml full. Now imagine that the master fader is also 10 ml in capacity. If you add 10 tracks, all 10 ml full, to the master fader glass, what happens? It overflows, and in the world of mixing, this is heard as distortion.
You may have maxed out the volume on each individual track, but you also have to control how much you send out to the master outputs. This is where each individual track fader comes it. To continue with my fluid analogy above, the track fader controls the flow of volume going to the master fader so that it doesn't 'overflow'.
This is how you should treat mixing. We may say set your track levels to this or that dB or say peak at this max dB per track, but your basis for the mix should always be the master outputs, not each individual track. As I'm fond of saying, "let your ears, and not your eyes, be your guide whenever you mix."