"The summit of Winking Isle is two dozen paces across... In the very centre stands a Well of black brick. As you cross the grass, scents arise: crushed flowers, camphor, ice."
"There may, or may not be, a lighthouse."
Winking Isle is a desolate speck of rock in the middle of, well, nowhere. It was the previous home of the entity now known as Mr Eaten.
The few Seekers lucky enough to visit this isle before the unfortunate occurrences leading up to December 9th, 1891, spent quite a bit of time fasting and meditating for Mr Eaten. They offered their most prized possessions in sacrifice. One perseverant visitor stayed long enough to obtain a couple of Mr Eaten's elusive candles. But several mysterious problems regarding occurrences on the island and the passing along of Mr Eaten's calling card (it seemed to create a duplicate of itself when given to another Fallen Londoner) led to the Masters halting all Mr Eaten-related activities indefinitely on the aforementioned date - December 9th, 1891. This moratorium ended (at last) on June 8th, 1894; it seems that after two and a half years, everything has finally begun running smoothly.
Somewhat lore-y details about the Isle, from its first visitor, are here:
Bug-related details about the Isle, from its last visitor (before 1894), are here:
Editor's note: I had to put a humorous, lore-connected spin on the Mr. Eaten hiatus somewhere. Regarding the rest of the storyline: it has an ending now, actually a lot of endings, but I won't put it anywhere here (even under a spoiler) until enough individuals have encountered it that it's no longer under wraps. I know Winking Isle has changed a lot as well, but please refrain from giving actual gameplay details, instead treating it like the actual history or nature of the island.