That kind of explains it all.
Basically, when the plane crashed in 2004, to the real world it appeared that it was in the ocean and everyone was dead etc. However, the plane actually crashed on the island and was sent back in time to the year 2000.
The button pushing keeps the island in its own timeloop i.e. time is frozen within that 108 minute stretch. When Desmond hits the failsafe, the year on the island is 2000 as is now the year in the real world (see new timeline). The island is also therefore visible to the outside world, hence Naomi is able to locate it.
As everyone was supposed to die in the plane crash in 2004, fate has a way of 'course correcting.' So the 6 that get off the island will eventually die before September 22nd, 2004 in the new timeline. Hence when we see at the end of season 3, Jack is at a funeral who we assume to be Sawyer's because of Kate's reaction.
The island will also be destroyed because in the original timeline, the plane crashed in the middle of the ocean where no island existed, so fate's course correction will lead to the island's destruction.
Least that's how I understand it
