This box is one of my most favorite origami boxes out there. This one is made by Tomoko Fuse who has made some amazing origami boxes in the past.
In Japan giving gifts is a big thing in their culture. The gift wrap, tsutsumi, is an important part of the gifting. People spend a lot of time on the wrapping part. Some gifts are placed in handmade origami boxes, called hakos.
The origami box shows the receiver that you took time to make the gift wrap yourself, and that you respect the person you are giving it to.
Go here for the diagram of the box.