An important part of the cowboy spur is the heel chain. Although this item is not really required to keep the spurs on your boots (depending on the spur design), it does add a little extra flash and show.
The spur heel chain is designed go around the back of the wearers boot but many of the normal sets of spurs you can buy are designed to use a spur strap or tiedown instead of the chain. The chains were possibly introduced to make the fit of spur more snug against the boot.
The heel chains were either made from silver or a cheaper metal. They are also of a very fine design and are not designed to withstand anything too rough. If you want to imagine what the chain is like, think of a slightly larger version of a silver necklace.