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 realises the brand is keep her 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.