The concentric circles form an eye - an open eye. They are the same open eye that we see in most episodes of LOST. We often see a close-up of a character's eye, typically in an episode that is central to that character. The opening of the eye represents something deeply intriguing in and of itself, but that is another story.
The outermost ring of the logo is a series of sixteen dots. They are the same color as the larger dot that serves as the pupil for the eye. What does this mean?
In LOST: The Complete Sixth and Final Season: Extras there is a segment entitled The Hero's Journey. In this segment, Damon Lindelof explains how Joseph Campbell's study of heroes in stories around the world influenced both Star Wars and LOST. Damon Lindelof speaks of the desire to create more than just one hero arc in this epic series...
Instead of saying "This is Luke Skywalker’s Journey" maybe we could do it with 16 heroes.
The road map for the character arc of the hero in LOST was planned around not just one hero, but sixteen.
The sixteen dots on the outer circle of the Oceanic logo represent the sixteen major heroes.
Jack, the primary hero, is represented by the central dot of the Oceanic logo - which symbolizes an eye. It is Jack's eye that we see open at the beginning of the series and close at the end. But he is not alone. He is surrounded by many others who also learn to open their eyes and truly see.