Confidentiality is the practice of keeping a revealed matter to oneself, i.e., as a matter of confidence.
Priests and lawyers are permitted by law to do this and cannot be compelled to give testimony to those who confess crimes to them. One of a Catholic priest's main jobs is to hear confessions and assign penance; if they had to report crimes to the police, far fewer people would dare to confess. A lawyer's ability to represent his client is greatly enhanced by his being able to communicate selective parts of what he knows of his client's history.
Physicians are required by law, in most jurisdictions, never to disclose details of a patient's illness or injury, or how such illness or injury came about, except only by the patient's consent (and to those to whom the patient permits the physician to disclose this information), or except under specific circumstances prescribed by law. The chief federal extension of this legal principle of confidentiality is the Health Insurance Portability and Accountability Act (HIPAA), which requires those who keep and maintain medical records in any form, paper or electronic, to guard them carefully against unauthorized access or disclosure.