I think that the question of "What exactly was the sideways timeline?" is a legitimate one. Sure, at first glimpse, most people's gut reaction was "it was purgatory", but I'm going to try and convince you of something different altogether (and hopefully it will fall into context of the show where you will see WHY I'm making the argument that I am).
OK. So the popular theories being floated around before season 6 is that LOST was going to end with a loop of some sort. That Jack was going to wake up in the jungle in the final scene, and the last scene would basically be the first scene. That was proven to be wrong, in fact, quite the opposite. HOWEVER, it doesn't mean that this loop didn't exist.
I'm a firm believer that this isn't the first time the losties have experienced the island (or at least all the characters they encounter on the island in some shape or form). They seem to have a hidden knowledge of events, especially Locke; a certain intuition if you will. I think that Desmond has always gone on this journey and has constantly been tested in every iteration and his main goal isn't a selfish one, but as a guide. He is the Buddha in the story, helping whoever wants to be helped, reach their enlightenment. And Daniel was always the one to help the losties establish this new life (with the bomb, or some other mechanisms that he could have used in previous iterations).
So after the bomb went off in season 5, the bomb worked EXACTLY how Jack thought it would. It got them off the island. It is 100% real (Keamy was killed in this life, Aaron was born, David is real). I think that this is just another "life" for the losties in the way people believe in reincarnation. The only people that "died" were the people in the church at the end. These are the people that "let go" (and I'm going to assume that Desmond is the exception...he is a godlike figure who exists simultaneously in all iterations of life).
I think people who experienced the "island deja vu" were the only people to die. At those moments, their life literally flashed before their eyes (and not just their fickle sideways lives or their more purposeful island lives, but ALL their lives that they've been through). Only after they all met up at the church were they able to finally "let go" and end their loop. In the words of Jacob "it only ends once"...but this theory is assuming there will be more loops with Desmond as the guide, Daniel as the catalyst, Ben searching for redemption, and Eloise, who knows about the past iterations but still can't imagine crossing over without her son.
I hope I made this clear enough for people. I'm not advocating this as an end-all-be-all and saying "if you thought the sideways was purgatory was stupid", but rather as an alternative theory explanation of how one could look at it.