Question

why does a pole star appears fixed at one point​

Answer 1

Polaris, located almost exactly at the north celestial pole, the center of spin, stays in the same place, while stars farther away from the north celestial pole can be seen to move in a wider circle around Polaris as viewed from Earth during its daily rotation.

Answer 2

The pole star is situated in the axis of the earth. When the earth rotates on its axis the pole star appears to remain stationary because the position of the earth isn't changing much with the respect to the star. So , no matterwhere we are in the earth and no matter what the time is , the pole star will always be on the same position, i.e. the axis of the earth.