While there is no scientifically agreed upon definition, and even some debate if such a thing exists among academics, the general consensus is that "brain washing" is a means of forcing people to submit or assent to direction to change the thought processes which govern their behavior and exchange their previous convictions for a new set of views and behavior patterns.
The "forcing" part is usually by means of threat, usually of pain/torture, even death. In exchange for being guaranteed that they will be spared from the threat, the subject submits their assent to the demands of the one in control.
The assent usually involves a systematic education and training program in which the individual changes their way of thinking and acting, being educated in the discipline of fighting any threat to their new conditioning.
"Brain washing" is considered complete when the subject follows the demands of the controller even when that party is no longer present or even dead. A person who is "brain washed" may not be able to function as normally as before even after deprogramming.
Those academics which agree that the situation is real or at least possible often add that it takes an educational background in psychology to properly brain wash a subject. Others suggest some people may have learned to be manipulative enough of others to perform a similar type of "brain washing."
Other experts disagree, focusing on the fact that assent of the subject is always required to some degree, and therefore at its core no one is actually "brain washed," merely willing to give up certain freedoms to avoid the threat placed upon them.
In my humble opinion, the amount of personal assent is not the issue as much as the training that is designed to keep people from realizing the threat may not be real or that they can freely choose not to assent without suffering in some instances. When this occurs, when the threat is a lie and people are trained to fight doubt and the understanding that they can be free whenever they want, then I think "brain washing" is what we're looking at.
But until it can be established by critical methods, "brain washing" is merely hypothetical and not theoretical (which it would need to be in order to be argued about in a court of law).