I only have a little bit of time but here it is:

The Earth's axis of rotation on itself is slightly tilted when compared to its axis of rotation around the Sun.

This changes the angle at which the Sun's rays hit certain parts of the Earth and causes the northern and southern hemispheres to experience seasons. In the northern hemisphere in summer, the rays are more direct and concentrated, causing a warming, in winter they are more oblique and less concentrated, causing winter.

Without this tilt, there would not be any seasons. The north and the south would always be colder than the equator which would probably be so hot that nobody would live near it.

Now to the link with sea ice

The large amount of ice near the north and south poles are very heavy, we are talking insane numbers here. This extra weight sitting at the poles has an effect on the angle of the Earth's rotational axis. If the ice melts, that weight is reduced and COULD change the angle of rotation of the Earth.

If the angle is reduced

Northern countries like Russia, Canada, Northern USA and Northern Europe will experience warmer winters, possibly no winters at all while warm countries closer to the Equator (Spain, Most of Africa Africa, the Middle East, China, Australia, India and their neighbors would experience much warmer weather, possibly causing these countries to become inhabitable, resulting is a large scale movement of population towards the more habitable countries.

If the angle increases

Then Northern countries will experience longer, colder winters, we are talking very cold to the point where growing crops will become almost impossible and life would be like living close to the North pole. Countries like Spain might experience winters similar to what is seen in Sweden and Northern Africa and the Middle East will also get colder.

That's all I have time for now.