A wire trace is the safety link between your hook and mainline. On the one end, the trace's swivel connects to your mainline. If you are fishing with lures, the other end will have a snap link swivel, which you can attach your lure to.
Traces can be utilised in many ways. You can use a heavier length of line protection from abrasion, you can use wire trace to protect from toothy critters or in some cases you can even use a lighter line than your mainline.