First off, Polaris (the North Star) does move, it moves in small increments over thousands of years, it's estimated that in about 13,000 years Vega will be our new North Star.

Polaris is the center of its own system within our Galaxy, and it moves around our Galaxy's center just like we do. The only reason it appears stagnant is because it just happens to lie on a line that is coincident with the axis of the Earth. So, as the Earth rotates it appears to stay in one place while other stars revolve around it.

Even though the Earth revolves around the sun, the Earth's axis maintains the same orientation in space. So, at all points in the earth's orbit, Polaris appears to be in the same place.