The 8 symbols on the octogonal logo found in the bunker and on the shark are I-Ching Trigrams (like the tattoo on the GI-Joe Snake Eyes!) They represent (starting at the top and around clockwise) South, Southwest, West, Northwest, Northeast, East, and Southeast. ( http://www.sacred-texts.com/ich/img/pl3-2.jpg) (the symbols in the logo are upside down, but still in order)
each trigram also has a number of different meanings, most apply to the show. (numerology, divinity, balance of good and evil, bla bla bla) Making it hard to pinpoint their exact importance.
I think some of the more interesting associations are between this symbol and the Korean peninsula. A Korean connection would also explain the Russian weapons... since North Korea was supplied by the Soviets. There's also the fact that the South Korean flag uses the same trigram symbol. Jin/Sun connection maybe?
One of the other theories I think is interesting is that the overriding idea of the symbol is balance, and the trigrams seem to associate with different people on the island. One section is associated with family (Claire, Jack, Sawyer, etc...), one is Fame (Charlie)... one is wealth (Hurley)... Maybe the island is trying to achieve "balance" by brining all these people there...
It's also a very "puzzle-like" image... the people are the pieces of the puzzle.
There's also some indication that the layout of the hatch space, in particular the "dome", is very similar to that symbol.
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