This image explains it well imo;
http://4.bp.blogspot.com/-jLlRGBHYzm4/UN18PluygVI/AAAAAAAAAcI/zSy1XyieAcc/s1600/14+Bit+Depth+03.jpg
Essentially one bit gives two possible states; on and off, or black and white. If you have two bits you have four possible states (both on, both off, first bit on and second bit off, or first off and second on) so you can have black, white and two shades of grey in between.
The more bits the smoother the gradient you can achieve.
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