Here's my guess:
Insert the strap through the tag until it reaches the end of the strap with a rectangular end. Next, pass the narrow end of the strap through both of the two slits in the rectangular end (one over, then one under). Pull it tight.
You can then use attach the tag to your luggage just like you did last year, by passing the tag back through the long slit and pulling it tight (after passing the strap through your luggage handle, of course).
I hope I didn't make it more confusing.