The US military operates bases and other installations located in remote, inaccessible regions – not only abroad, but also within US states and territories. Supplying these sites is often a formidable task, especially when it comes to heating and electricity.
In the case of Eielson AFB, this means regularly hauling in tonnes of coal to provide it with 33.5 MW of electricity. Aside from the environmental impact, it's also expensive, a logistical nightmare, and ties up personnel better employed elsewhere. This isn't unique to the Alaskan base, so the Air Force is interested in looking at nuclear energy as a cleaner and simpler alternative.