Imagine that you live in Joliet, IL (latitude 41.5 degrees North). Assume that the Earth continues to orbit the Sun as it does now. You find your seasons have
changed such that you (and everyone else at 41.5 degrees North latitude)
experience a day with 24 hours of continuous daylight and six months later a day
that has 24 hours of continuous darkness over the course of a year. How would this
be possible?

About a 24 hours of daylight and 24 hours of darkness can be seen at poles.

The earth has an elliptical orbit and it rotates around the sun. This rotation may diffident from time to time as some times its closer and some times it is far from the sun.

if we assume that I live in Joliet IL and the place has a latitude of 41.5 degrees to the north. Then assuming that the earth is revolving around the sun and has different seasons. The seasons change as per the direction and position of the earth from the sun. The earth has 24 hours of the day.

Thus earth has an equal amount of 24 hours of darkness and 24 hours in daylight at the north and the south poles. This is seen six months later.

Find out more information about the earth's orbit around the sun.

link.