Well a fusible link is just a special section of wire that is mean to burn up when there is a short circuit to protect the rest of the wiring. It has a fire resistant insulation so that when the wires inside burn up, the insulation stays intact. One good way to check fusible links is to pull on them with a moderate amount of force, and if its bad, the insulation will break. A fusible link will always 4 wire sizes smaller than the wire it is attached to.
All of the power that goes to your car comes off that fusible link, the other wire just powers your starter.
With that said, its probably not the fusible link itself, but more likely the crimp connection of that wire to the main battery positive. Is there any tape or insulation that might be hiding a problem under there? Are your battery connections all factory or have they been replaced?
Hope this helps
Ryan