Why is it important that farmers plant crops during the winter that improve the levels of nitrogen in the soil?
these crops can fix nitrogen into usable nitrates.
these crops have root nodules that contain bacteria.
these crops produce fruit that quickly decomposes into usable nitrogen.
these crops all use nitrogen in their specialized photosynthesis process.

These crops can fix nitrogen into usable nitrates.  

Explanation:

There are certain crops which are called cover crops, specifically legumes like peas, vetch,clover and winter field beans . Farmers grow these crops during winter before the growth of actual target crops like cabbage etc which are thirsty for Nitrogen.

What is special about these cover crops is their ability to fix nitrogen into the soil from the atmosphere. There are various ways through which these leguminous crops can fix nitrogen into the soil:

This phenomenon confers the leguminous crops with an ability to fix  nitrogen in the soil that can be used by the nitrogen requiring crops like cabbage when grown next season in same soil.

Hope it help!