Stick a small paper sticker on the globe at your own town. Now look down on the globe from straight above the North Pole and turn it slowly anti-clockwise.
Observation: the sticker does not go up or down — it travels along a circle, parallel to the equator, and after one complete turn it arrives back exactly where it started. Every other point of the globe does the same thing on its own circle, and all these circles have their centres on the axis.
Why it happens: that is precisely what rotation means — all parts of the object move in circles about an imaginary line passing through it. The two points that do not travel at all are the North Pole and the South Pole, because they lie on the axis.
Try this: stick a second sticker near the equator and a third close to the North Pole. In one turn both complete a full circle in the same time, but the equator sticker covers a much bigger circle — so a place on the equator is actually racing through space much faster than a place near the pole.