For this particular version I used a cotton print. I’ve also made a sturdier version out of faux leather (pinking the edges instead of fraying them) that I used as fancy gift wrap for a set of bar utensils.
See fraying tips here. Because this was part of a wedding gift—a picnic set for two—I only created two utensil sleeves, and put two forks in one sleeve and two knives in the other. This is totally flexible though, and can change to suit your needs.
All wrapped up, with places to go:
Picnic roll and matching set of frayed-edge napkins: