Shipping fever is actually a form of pneumonia that is observed in horses that are shipped long distances - and which can even be fatal.
What causes it is a combination of dehydration (horses not being watered often enough), inadequate ventilation and being tied up for extended periods of time. Oh, and stress. All of this lowers a horse's resistance to infection. The risk really starts with journeys of three hours or more.
It is prevented in part by avoiding shipping sick animals (except to a hospital if necessary). If you see a trailer has all the windows open in the middle of winter, that's actually correct - horses feel the cold less than we do and need their ventilation. Hay should be soaked (which cuts dust and reduces dehydration) and low dust bedding should be used. Regular rest breaks also help. In some cases, it's possible to trailer horses loose (always a better option as they're also less likely to fall that way).