First of all, the North Star is not the brightest star in the sky–not even close. Its formal name is Polaris and at magnitude +2, it barely makes the top 50 brightest stars in the sky (#48, not including the Sun).
Secondly, Polaris is not the closest star to the Sun, being 430 light years away. Its relatively bright nature is due to its luminosity. Polaris is a yellow giant star 2500 times more luminous that the Sun, 6 times as massive as the Sun, and a diameter 45 times that of the Sun. If Polaris were put where the Sun is, its surface would be more than half the distance to Mercury.
Thirdly, Polaris is actually a triple star system. The two companion stars are very faint and very close making them extremely difficult to resolve by the backyard astronomer. Polaris is also a cepheid variable, with an imperceptible variability of 0.03 over its 4 day period.
Lastly, Polaris not exactly above Earth’s North Pole. At declination 89.18°, it is so close to the north celestial pole, that to the casual observer, it is the only star that doesn’t move over the course of an evening or from night to night. Polaris has been an important navigational star as its measured angle above a flat horizon approximates the observer’s latitude on the Earth. Of course, from the Equator south it is not visible. Because of the precessional wobble in the Earth’s rotational axis, Polaris will not always be the North Star. Around the year 2105, Polaris will be as close to the north celectial pole, 1/4° away, as it will ever get. After that it will move further away and eventually, there will be no ‘north star’ in the sky.