Before the definition of the Arctic was formalized as the region north of the Arctic Circle which experiences the Midnight sun, it more broadly meant those places where the 'bear' constellations (Ursa Major, the Great Bear, and Ursa Minor, the Little Bear) were high in the sky.
Stars far from a celestial pole appear to rotate in large circles; stars located very close to a celestial pole rotate in small circles and hence hardly seem to engage in any diurnal motion at all.
The circumpolar stars appear to lie within a circle that is centered at the celestial pole and tangential to the horizon.
[1] As one travels south, the north celestial pole moves towards the northern horizon.
Polaris itself remains almost stationary, always at the north (i.e. azimuth of 0°), and always at the same altitude (angle from the horizon), equal to the observer's latitude.
[3] Since the altitude of the north or south celestial pole (whichever is visible) equals the absolute value of the observer's latitude,[3] any star whose angular distance from the visible celestial pole is less than the absolute latitude will be circumpolar.
At the North or South Pole all stars that are visible at all are circumpolar, since only one half of the celestial sphere can ever be seen.
Thus, Canopus is invisible from San Francisco and Louisville, Kentucky, if marginally visible from Fresno, Tulsa, and Virginia Beach.
[3] For British Isles observers, for example, the first magnitude stars Capella (declination +45° 59′) and Deneb (+45° 16′) do not set from anywhere in the country.
Vega (+38° 47′) is technically circumpolar north of latitude 51° 13′ N (just south of London); taking atmospheric refraction into account, it will probably only be seen to set at sea level from Cornwall and the Channel Islands.
As viewed from the North Pole, all fully visible constellations north of the celestial equator are circumpolar, and likewise for constellations south of the celestial equator as viewed from the South Pole.