Wat is the relation between north and south poles n circle of illumination on march 21 n September 22?

Those two days are respectively the spring and the autumn solstices. The sun is then perpendicular (at the zenith) of the equator. On both poles, the sun is exactly on the horizon during the entire day. In fact, both poles have, alternatively a day of six months and a night of six months. At the solstices, they have both a sunrise/sunset of 24 hours.