The phrase "extensive background" refers to a person's or thing's past experiences, knowledge, skills and qualifications. It can also refer to an in-depth investigation into someone's history, including their personal life, education, work experience, criminal record, financial records, etc., in order to determine their suitability for something such as employment, a loan, or a security clearance. In other words, it means having a lot of information about someone or something that helps to form an opinion or make a decision.