A Methuselah Binding refers to a binding cast by a djinn in attempt to keep someone in their place. The binding causes the person (or djinn) affected to age at a very rapid rate. Layla Gaunt used this on her husband, Edward Gaunt when she wanted to stop the twins from stopping her from becoming the Blue Djinn of Babylon. As a result, after the twins returned from rescuing Mrs. Gaunt they saw that the binding had caused him to age considerably. Fortunately, the binding was able to be reversed and Mr. Gaunt returned to his normal self.
The name of the methuselah binding comes from the oldest person mentioned in the Hebrew Bible. Methuselah. It can also be used to descibe someone living until a great age, such as in the case where Mr. Gaunt grew older when left by his children.