In the Cold War, Soviet subs, ships, and planes would have needed to pierce the Greenland-Iceland-UK Gap where NATO maintained a barrier to threaten the sea line of supply. Iceland was a key outpost in that barrier.
While the threat is much lower now than in the Cold War, our assets to move forces and supplies are thinner on the ground (so to speak).
And Iceland is virtually undefended (just a Coast Guard with 130 personnel in 2012). So NATO's renewed attention to Iceland is good:
Iceland may not have a navy, but the strategically located small nation is punching above its weight in terms of sea control and maritime safety in the increasingly important North Atlantic region, the head of U.S. naval forces in Europe said.
Right in the heart of the Greenland-Iceland-United Kingdom gap, Iceland is at the forefront of a boom in travel to high-north destinations, a growth in commercial shipping as North Atlantic and Arctic sea lanes open up, and an increase in Russian submarine activity.
In a nod to the importance of the country, Adm. James Foggo, the head of U.S. naval forces in Europe and Africa and the commander of NATO’s Allied Joint Force Command Naples, stopped by Iceland for the kickoff of the Trident Juncture 2018 exercise.
I assume that contingency plans put an American Marine brigade in Iceland to be relieved by an Army National Guard brigade after mobilization.