If a man suspected his wife of infidelity and had warned her not to go with a certain man, and she refused and went somewhere together with him, yet the husband had no actual proof she was unfaithful because in Jewish law we never usually accept circumstantial evidence. He could bring her to the Priest who then would question her. If she remained adamant that she was innocent, she was given some holy water to drink into which Gods written name was dissolved, with some dust from the Temple floor. The Priest then warned her that if she was guilty then the water would have a very bad physical effect on her.
The trial by ordeal was a feature of Western legal systems until early modernity. Whether witches or adulterous wives. Wherever the situation was unclear and with no obvious evidence, trying by torture or other means to solve the problem was common even if we probably knew that this was a cruel and completely unreliable process. Trial by ordeal was common in Europe and America until the seventeenth century.
In the same way, they used to rely on oaths in the absence of proof. Nowadays we still use oaths in courts eve if we know that most people ignore them.
We can understand now that this was a perfect example of psychological intervention and the waters had an effect it would be psychosomatic illness. The idea was to use whatever religious means one could in these early societies, to pressurize the woman either to admit or to seek some way out of an unhappy marriage. The priest in addition to his official religious functions also was a sort of psychotherapist and marriage counselor.
Still it seems unfair that women should be subjected to this ordeal and not men. But according to the Talmud if a woman drank the water it would affect the husband too. If he had been unfaithful he would also be physically affected as well. At least this goes some way towards leveling the playing fields.
As long ago as two thousand years ago, Rabban Yochnan Ben Zakkai stopped this institution of the Sotah. He said that since the men at that time were in general neither more faithful nor honest than their wives he saw no reason for them to have this right the bible gave them over women. And since then it has never been used (some people think it never was). But it remains as a warning to us all about the importance of openness, honesty and fairness in a relationship.
Have we changed much since then?