This picture showed up on Reddit with the title “Because fuck everybody,” and after I stopped laughing, it piqued my curiosity.
As it turns out, this is the island of Elliðaey (63° 28’05.10″ N, 20° 10’31.98″ W), the third largest island of the Westman Islands, located south of Iceland. The island is a mere 0.18 mi² in area and is uninhabited. From this website, we learn the following information (translation is mine, so it’s imperfect but gives the gist):
“On the island is a large fishing house owned by the Ellidagrim Islands Society, which engages in puffin egg hunting in summer and in spring. In earlier times there was a hunting lodge called simply “dwelling.” The first building which was built on the island still stands. It is used for storage, and is west of the ‘Skápana.’ In 1953, a new lodge was built at the foot of Hábarð (the highest peak on Elliðaey) because the old building failed the test of time. In 1985, work began on a new two-story fishing house which was attached to the house that was built in 1953; it was completed in 1987. In 1994 it was discovered that the 1953 edifice had deteriorated to such an extent that it was no longer useable. It was therefore demolished and another house built instead in the same location, with construction being completed in 1996. Between 2000-2001, a small house west of the lodge was built, which houses the Ellidagrim Islands Society sauna.”
A recent picture showing the 1996 lodge, and the small sauna finished in 2001.
There’s a lot of misinformation out there about this island, chief among which is that Iceland gave Elliðaey to the singer Björk as a royalty payment for her services to the nation.
From “The Independent”, 2-10-2000:
THE ICELANDIC singer Björk may have put her nation on the map, but plans to grant her exclusive use of an uninhabited island off the west coast to reward her for her services have run into difficulties.
Earlier this week David Oddsson, Prime Minister, told parliament: “Björk has done more for the popularity of Iceland than most other Icelanders. My view is that she may be given the use of this island [Ellidaey] as a royalty payment, as recognition from the state.” But, amid an uproar in the country, the government has had to reconsider its generosity. Yesterday Mr Oddsson’s office denied Ellidaey had been sold or leased to the singer. If sold, said a spokesman, it would be only to the highest bidder. Icelandic radio reported rumours that the musician was no longer interested in the island. She has neither confirmed nor denied reports and was not available for comment yesterday. Despite her much-professed love for Iceland, Björk is neither based there full-time nor does she sing in Icelandic.
Notice that the Independent article says “off the west coast.” The confusion arose because there is another island with the name of Elliðaey to the west of Iceland (65° 8′ 42.86″ N, 22° 47′ 10.99″ W), just north of Stykkishólmur,
which is most likely the one referred to by the Prime Minister in his abortive but generous gesture. Mr. Oddsson thought it would be a nice idea, but local protests deep-sixed the plan. As for the island of Elliðaey to the south, the one with the hunting lodge, it was never associated with Björk in any way.
The Old Wolf has spoken.
 No idea what this refers to.