Desmond has given us clues by ali

When Juliet set off the bomb it was similar to what happened when Desmond turned the fail safe key (as some have written, the fail safe may have actually been the Jughead). When Desmond's consciousness traveled through time he was in the time he traveled to - and he was also disoriented. He knew what was going on, both when he traveled back and woke up in his apartment that hie was painting, and when he traveled back and woke up in the army. But there were clues that he was time traveling, and things that he experienced as deja vu, like the beeping of the microwave, seeing Charlie playing on the street corner, and hearing the song on the jukebox.

This is what is happening to Jack and Kate in the new timeline. When the bomb exploded their consciousnesses traveled back to the airplane. They are oriented to the time they are in, 2004, but they are also disoreinted. The bomb also caused things to change back in 1977 and we are seeing those changes in this new timeline (like Hurley being lucky, Desmond on the plane, etc.). They are different people also because they have changed over the past three years and through their interactions with each other. They also seem to recognize each other, and to recognize other things (like Claire, Aaron's name, and the stuffed wale).

Whose consciousnesses traveled? Everyone who was at the bomb sight - or just Jack and Kate? Jin, Sun, Sawyer and Hurley don't seem to be exeriencing deja vu... What about Rose and Bernard?

I wonder if the bomb caused the Losties (or at least jack and Kate) to time travel, and cased things to change. Their consciousness traveled back to the plane in 2004 - the plane now in the changed timeline. And then, their consiousnesses came back to 2007 on the island. It seems like things haven't changed in 2007 on the island but perhaps they have. Perhaps because the universe has a way of course correcting they end up in the same place anyway. How they get there will be different, but it leads to the same basic circumstances. The thing that gets in the way of this theory is that the Island is sunk in the new time line... can't explain that, yet.