Why doesn't Polaris seem to move?

The apparent "movement" of the stars through the night sky is due to the rotation of the Earth. The observer on Earth is going around in a big circle every day. The center of that circle is the axis of rotation of the Earth. (The longer term movement due to the orbit around the Sun every year does not affect the apparent position of the stars because they are so far away.)

Polaris is (almost) in line with the Earth's axis of rotation. At night, as the Earth rotates, Polaris appears to stay at one point in the sky as the sky rotates around it. That point is the North Celestial Pole.

Polaris is used for simple navigation because it is at a height in degrees above the horizon equal to your North latitude. (At the North Pole it would be straight up, so 90 degrees. In London, for instance, that number is 51½ degrees.)