Sotah, Chapter One, Mishnah Four
The mishnah now begins to describe the process of bringing the sotah to the Temple. First the judges warn her just how serious the ceremony and its consequences are. The point of this admonition and of all of what they say to her is to convince her to admit to her guilt so that the name of God will not be rubbed out from the scroll onto the water, as mandates the ceremony.
They bring her up to the great court which is in Jerusalem, and [the judges] solemnly admonish her in the same way that they admonish witnesses in capital cases.
And they say to her, My daughter, much is done by wine does much, much is done by frivolity, much is done by youth, much is done by bad neighbors. For the sake of His great name which is written in holiness do it so that it may not be rubbed out on the water.
And they say to her matters which neither she nor all the family of her father’s house is worthy to hear.
In capital cases, the judges warn the witnesses that if they testify falsely, an innocent man will be executed. Similarly, here they warn the woman, that if she lies drastic results will occur. For the warning given to witnesses, see Sanhedrin 4:5.
The judges also tell her that many things might have caused her to commit adultery and while these do not excuse her sin, they make her sin more understandable. They are telling her that she should not be shamed of admitting her guilt. They implore her not to go through with the ceremony, because part of the ceremony involves writing Gods name on a scroll and then rubbing it out. This is a great desecration and should only be done under the most dire of circumstances.
Finally, they tell her things which the mishnah doesnt even want to mention. Note that according to the mishnah, her family came along with her. Assumedly they are there to defend her, and hope that she is found innocent.
The Talmud relates that they tell her stories where Biblical characters admitted to their sins. For example, Judah admits that he sinned with Tamar (Genesis 39:26).