A binding link is a symbol which keeps a demon trapped inside its meatsuit i.e. the human it is possessing. The demon can neither escape voluntarily or be exorcised. A binding link may be related to the "binding magic" used on curse boxes to keep the evil inside.
When Meg possesses Sam she brands a binding link into his forearm. When Bobby tries to exorcise her, it doesn't work. Bobby realizes the brand is keeping the demon trapped inside Sam, and burns across the mark with a hot poker, breaking the spell.
- Crowley: This bit of carving will tie our friend here down. No zapping off, locked in the meat suit. An important part of our bargaining strategy.