The fusible link is basically standard stranded wire, with a special high temperature insulation that resists the heat during failure, in order to contain the arcing and burning that occurs when the link opens. The material differs from the standard wire insulation on the wire harness wiring. There are markings on fusible links that indicate the wire gage, along with the designation "Fusible Link" (makes it easy to spot).
Links are there to prevent dead short circuits, which would result in burned wiring within the harness. They contain the "fire". In fact, when a link fails, you can usually see slight indication outside of the insulation, not a major burnout.