Tsutsumi means to wrap, cover, conceal.
In Japan gifts are always packed with great care and a simple yet artistic flair.
The term probably refers to the traditional practice of wrapping items with cloth squares (furoshiki) but it's also used for paper wrapping.
(By the way, if you have an iPhone, check out the Furoshiki Guide for iPhone)
I have recently started exploring this as an alternative to western-style gift wrapping (especially because I am pathetical at making packages).
And remember, there are Tsutsumi Gods walking among us: