Family law by its very nature involves personal, private, and sometimes embarrassing facts. People are naturally reluctant to reveal these details; especially to someone they just met. The attorney-client privilege is meant to protect confidential communications between you and your attorney when they relate to seeking legal advice or preparing for your case.
The idea behind the privilege is that a client has a right not to disclose any confidential communication made to their attorney. The communication must be confidential and must be made in a professional capacity. The privilege belongs to the client and only the client can waive the privilege. One way to waive the privilege is to tell someone else what you and your attorney discussed. The privilege only protects the communication itself and not the underlying facts. For example, you could tell your lawyer about an affair you had, but the fact that you had an affair is still admissible.
In addition to the attorney-client privilege, lawyers are required to keep their clients communications confidential. Lawyers are bound by rules of professional conduct that regulate how they practice law. The ABA Model Rules have been adopted in whole or part in many states. Under the rules an attorney is required to keep the confidences of their clients except in certain situations (such as to prevent a reasonably certain death). Tennessee is a state that has a similar rule: RPC 1.6 Confidentiality.
This post cannot possibly cover all of the rules and nuances of the attorney-client privilege, but your attorney will be able to give you his opinion on what is covered. The privilege is a powerful tool that allows clients to openly discuss their cases with lawyers without worrying about the details being repeated to their family and friends. Your attorney is there to help you get the best possible result in your case; if you hide information from them because it is embarrassing, it only means that they will not be prepared when this fact later is brought up at trial by the other side. You do not want your attorney to be surprised at trial. If they know about the fact in advance they can prepare for it and perhaps lesson its sting.