What determines where the Arctic Circle lies?

The Arctic Circle lies at 66° 30′ north latitude.

This is because that is the southernmost latitude where the sun can be seen for a full 24-hour period on or about June 22, the first day of summer (summer solstice).

On the same day in the Antarctic Circle (south of 66°30′ south latitude), the sun does not shine at all.

The situation is reversed during the winter solstice.