What is Respondeat Superior?

Legal Definition
Respondeat superior (Latin: "let the master answer"; plural: respondeant superiores) is a doctrine that a party is responsible for (has vicarious liability for) acts of their agents. For example, in the United States, there are circumstances when an employer is liable for acts of employees performed within the course of their employment. This rule is also called the master-servant rule, recognized in both common law and civil law jurisdictions.

In a broader scope, respondeat superior is based upon the concept of vicarious liability.
-- Wikipedia
Legal Definition
A legal doctrine, most commonly used in tort, that holds an employer or principal legally responsible for the wrongful acts of an employee or agent, if such acts occur within the scope of the employment or agency.
Legal Definition
Let the master answer. This maxim means that a master is liable in certain cases for the wrongful acts of his servant, and a principal for those of his agent Broom, Max. 843. See Southern Ry. Co., v. Morrison. 105 Ga. 548, 31 S. E. 564; Haehl v. Wabash R. Co., 119 Mo. 325, 24 S. W. 737; State v. Gillespie, 62 Kan. 469. 63 Pac. 742, 84 Am. St. Rep. 411.
-- Black's Law Dictionary
Legal Definition
The superior is responsible, i. e., the employer is responsible for the act of his employee. See 119 Mo. 325, 24 S. W. 737.
-- Ballentine's Law Dictionary