You will see them a lot at flyball matches. They are these durable, braided fleece tug toys that handlers use to catch their dogs at the end of a run. Those tugs take a LOT of abuse. They have enough give to act as shock absorbers when the dog hits the end of the tug at full speed, but are strong enough to stand up to hundreds of those type of hits. People also use them at agility matches as a tug reward at the end of a run. They can be a bit hard to find. In the pet stores they just have the standard three-strand fleece braid toys and those are short, overpriced, and don't last nearly long enough.
Here I will give you step-by-step instructions on how to make that square or "box" braid so that you can make your own, in whatever custom colors you and your dog agree on.