This is because the Earth's axis is tilted at an angle of 23.5 degrees. This tilt causes the Sun's apparent position in the sky to change throughout the year, leading to the seasons. On the Summer Solstice, the Sun reaches its highest declination (angular distance north or south of the celestial equator) of +23.5 degrees.
Therefore, the angular distance between the North Celestial Pole (which is at 90 degrees declination) and the Summer Solstice (at +23.5 degrees declination) is 90 - 23.5 = 66.5 degrees.