It depends.
There is an attorney-client privilege that covers private and confidential communications made between an attorney and his client, when these communications are made outside the presence of others and relate to the legal services being performed for the client by the attorney and relate to legal proceedings. What is said cannot be disclosed by the attorney without the permission of the client.
An attorney can be reprimanded or suspended or disbarred, in other words, for speaking publicly to others about his client and his client's personal and confidential affairs.
But there are exceptions to this privilege (ie. if a client communication relates the committing of a future crime) and this privilege can be waived under other circumstances (ie. if the client speaks to others about what he has said to his attorney). And if an attorney is acting merely as an advisor, privilege will generally not apply.