When you listen to the album in its entirety, you can feel the story behind the songs. You experience the struggle of love in a time of hardship and the hope for a brighter future.
Not many bands and artists commit to the tall-order of making a concept album anymore. But Coldplay did, and they did it in such a way that is truly tremendous.
Also, I love all of the Peter Pan references. Simply another way in which these songs fly you to another world.