Authority is the ability to exert power over another. Under Capitalism this often comes with some mechanism of enforcement. The State exercises authority over its citizens, enforced by the police and courts. But even without coercion or enforcement, doctors can exercise authority over their patients.
Recognising authority as a part of life, Anarchists believe that all authority should be defined by, accountable to and recallable by those who fall under that authority. In this way, capitalists, cops, courts, landlords, etc all fail the burden of proof, but doctors, teachers, experts, etc may be able to meet the Anarchist idea of justified authority.