Lots of people seem to only really read the first volume, which kind of disappointing because the first volume alone is really is only keyhole into the true beauty of the series. There are many reason as to why I think this series is my favorite, but to things (relatively) short, I'll just be focusing on the setting.
What I believe makes Utsuro no Hako outstanding is how perfectly the author executes the philosophical complexity of human nature with the environment the characters interact in. What makes this possible is how the author designed the functionality of a plot device called boxes. Boxes in the story allow the user to make any wish perfectly how they perceive it, including their doubt. This sort of concept gives the author the liberty to throw the characters into all sorts of creative scenarios without the reader feeling like the situation is unnatural. What has made many series appealing were their ability create arcs that could each function independently on their own, yet supplement the character development of the main cast in the overarching timeline. Consider a series like One Piece. Many enjoy the series because each arc provide an unique narrative, yet with each arc, you could see the more of the bigger storyline unfold. Same goes for Utsuro no Hako. Every volume or every few volumes will give you a engaging arc, but as you look at the bigger picture, you start to see how each of these arcs ties with the development of Kazuki and Maria.
As for the actual settings, damn are they interesting. Not only do each of them work under a unique concept, the intellectual depth provides you with sense of thrill you rarely get from most series that rely on have action scenes or emotional trama. If you read all 7 volumes, I'm sure you will be able to appreciate the series's ability to drive your emotions and intellect.