Shadowbinders are a type of sorcerer, said to hail from Asshai. They are practised in various skills involving the binding of shadows to do their will. R'hllor counts shadowbinders amongst his followers.
Stannis's shadowbinder ally is revealed to be Melisandre. The reason for the name is revealed when she draws on Stannis's life force to create two shadow creatures, one to slay his brother Renly and the other to kill Ser Courtney Penrose and secure the capitulation of Storm's End.
Melisandre tells the captive Ser Davos Seaworth that creating shadows is hard work, being extremely taxing on the person whose life force is being used to create them. Having created two from Stannis already, she could not create a third without it killing him. She suggests Davos could make the sacrifice instead, but he refuses her.