To cauterize is to seal off a wound or incision by burning it or freezing it, usually a hot iron, electricity, or chemicals. Metaphorically, it means to make less sensitive to feelings and emotions.
Cauterize is usually a medical term. In surgery, using an electrical tool to cauterize the incision seals off blood vessels, resulting in a cleaner operation that heals more easily. Extreme cold, electricity, and chemicals are also used outside the body cauterize, or "burn off," warts and vessels that cause nosebleeds.