The Doble test is basically a power factor test performed on transformers to ensure they are functioning correctly. This dissipation testing can also be performed on MV cables and motors.
Some techs use the term as a catchall phrase for a breaker's timing test using a shunt trip. Doble is actually an 85 year old diagnostic testing equipment manufacturer whose name has become synonymous with this form of testing. The company's goal is to assist those in the electrical power industry streamline operational improvements and increase performance of electrical equipment.