A Latin term meaning "in arguing" or "for the sake of argument". When one assumes something arguendo, the person is asserting a hypothetical or other statement for the purpose of argument.
Definition from Nolo’s Plain-English Law Dictionary
Latin for "for the sake of argument" used by lawyers in the context of "assuming arguendo" that the facts were as the other party contends, but the law prevents the other side from prevailing. For example, a lawyer might say at trial, "even assuming, arguendo, that the court finds our client, the defendant, was negligent, the other party was also so negligent that he cannot recover damages." In short, the lawyer is not admitting anything and wants only to make a legal argument.
John, a law professor, knows his student Judy is not married but John wishes to use Judy in a hypothetical to explain a particularly difficult point. John says, "Assuming arguendo Judy was married, would her marriage be valid?"