DarkUFO put together a poll of top Lost mysteries. One such mystery is What happened to Jacob’s cabin?
In comments bongzilla suggested Googling for Baby Yaga’s hut. Sure enough, that produced an interesting result at Wikipedia. I’m not saying Lost is following the legend faithfully, but it wouldn’t surprise me if the writers are borrowing pieces of the legend the way they’ve done with other legends and literature. Asterisks go to Lost connections.
Baba Yaga (Russian: Ба́ба-Яга́, Macedonian and Serbian: Баба Рога, Bulgarian: Баба Яга, Polish: Baba Jaga, Czech: Ježibaba (also: Baba Jaga), Slovak: Baba Jaga, Croatian: Baba Roga, Slovene: Jaga Baba) is, in Slavic folklore, a witch-like character who flies around on a giant mortar, kidnaps (and presumably eats) small children*, and lives in a house on chicken feet. In most Slavic folk tales, she is portrayed as an antagonist; however, some characters in other mythological folk stories have been known to seek her out for her wisdom, and she has been known on occasion to offer guidance to lost souls**, although this is seen as rare.
The name differs within the various Slavic languages. It is spelled “Baba Jaga” in Czech, Slovak and Polish (though Czech and Slovak also use Ježibaba). In Slovene, the words are reversed, producing Jaga Baba.***
In Russian tales, Baba Yaga is portrayed as a hag who flies through the air in a mortar, using the pestle as a rudder and sweeping away the tracks behind her with a broom made out of silver birch.**** She lives in a log cabin that moves around***** on a pair of dancing chicken legs, and/or surrounded by a palisade with a skull on each pole. The keyhole to her front door is a mouth filled with sharp teeth; the fence outside is made with human bones with skulls on top, often with one pole lacking its skull, leaving space for the hero or heroes. In another legend, the house does not reveal the door until it is told a magical phrase: Turn your back to the forest, your front to me.
In some tales, the house is connected with three riders: one in white, riding a white horse with white harness, who is Day; a red rider, who is the Sun; and one in black, who is Night. Baba Yaga is served by invisible servants inside the house. She will explain the riders if asked, but may kill a visitor who inquires about the servants.
Baba Yaga is sometimes shown as an antagonist, and sometimes as a source of guidance; there are stories where she helps people with their quests, and stories in which she kidnaps children and threatens to eat them.* Seeking out her aid is usually portrayed as a dangerous act.****** An emphasis is placed on the need for proper preparation and purity of spirit, as well as basic politeness.******* It is said she ages one year every time she is asked a question, which probably explains her reluctance to help. This effect, however, can be reversed with a special blend of tea made with blue roses.
There are indications that ancient Slavs had a funeral tradition of cremation in huts of this type. In 1948 Russian archaeologists Yefimenko and Tretyakov discovered small huts of the described type with traces of corpse cremation and circular fences********** around them; yet another possible connection to the Baba Yaga myth. 
Modern fantasy writers, such as Tad Williams and Elaine Cunningham use the character of the cabin on chicken legs in their works, as do Fritz Leiber (Fafhrd and the Gray Mouser) and Mike Mignola in his portrayal of Baba Yaga in his Hellboy comics. The castle in Hayao Miyazaki‘s film version of Diana Wynne Jones‘ novel Howl’s Moving Castle also moves on mechanical chicken legs.
*Women can’t can’t conceive and deliver children on the island.
**Ben takes Locke to Jacob to seek advice. Locke returns later to find Christian Shepherd and Claire, and is told he has to move the island.
***”Jaga Baba” is sorta kinda like Jacob, but I admit this is a stretch, especially since the little we know of Jacob strongly suggest he’s male, beard and all. I think the name Jacob is more likely to be based on Biblical mythology, which Lost follows in a big way with regard to characters’ names: James, John, Benjamin, Aaron, Michael, etc.
****The Others apparently cover their tracks by sweeping them with brush.
*****Much like the Losties have difficulty re-finding the cabin, which seems to move.
******Ben seemed to seek Jacob’s advice reluctantly.
*******Ben emphasized that Jacob didn’t like technology, so they stopped using flashlights and switched to a lantern before entering his cabin.
**********Jacob’s cabin is surrounded by a circle of what looks like ash. Possibly unrelated, but the Barracks are surrounded by a circle of sonic fence that keeps out the Smoke Monster who seems to have some parallels to Baba Jaga, based on the description of her flying around in a mortar with her pestle as a rudder, though that’s once again stretching things. I’m much more comfortable thinking of Baba Yaga as a broad inspiration.
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