Iceland, like Norway where I'm from, is part of the European Economic Area[1] through the European Free Trade Association[2], but not a full EU-member. They get access to the EU single market, by agreeing to implement EU legislation in a number of areas.
It can be quite confusing at times. For example, both Iceland and Norway are part of the Schengen agreement[3], so in that respect we're "from EU" when traveling.
Its incredibly useful for visa reasons though.