This is the law of jealousies, when a wife goeth aside to another instead of her husband, and is defiled;

Jamieson-Fausset-Brown Bible Commentary

29. This is the law of jealousies-Adultery discovered and proved was punished with death. But strongly suspected cases would occur, and this law made provision for the conviction of the guilty person. It was, however, not a trial conducted according to the forms of judicial process, but an ordeal through which a suspected adulteress was made to go-the ceremony being of that terrifying nature, that, on the known principles of human nature, guilt or innocence could not fail to appear. From the earliest times, the jealousy of Eastern people has established ordeals for the detection and punishment of suspected unchastity in wives. The practice was deep-rooted as well as universal. And it has been thought, that the Israelites being strongly biassed in favor of such usages, this law of jealousies "was incorporated among the other institutions of the Mosaic economy, in order to free it from the idolatrous rites which the heathens had blended with it." Viewed in this light, its sanction by divine authority in a corrected and improved form exhibits a proof at once of the wisdom and condescension of God.

Matthew Henry's Concise Commentary

5:11-31 This law would make the women of Israel watch against giving cause for suspicion. On the other hand, it would hinder the cruel treatment such suspicions might occasion. It would also hinder the guilty from escaping, and the innocent from coming under just suspicion. When no proof could be brought, the wife was called on to make this solemn appeal to a heart-searching God. No woman, if she were guilty, could say Amen to the adjuration, and drink the water after it, unless she disbelieved the truth of God, or defied his justice. The water is called the bitter water, because it caused the curse. Thus sin is called an evil and a bitter thing. Let all that meddle with forbidden pleasures, know that they will be bitterness in the latter end. From the whole learn, 1. Secret sins are known to God, and sometimes are strangely brought to light in this life; and that there is a day coming when God will, by Christ, judge the secrets of men according to the gospel, Ro 2:16. 2 In particular, Whoremongers and adulterers God will surely judge. Though we have not now the waters of jealousy, yet we have God's word, which ought to be as great a terror. Sensual lusts will end in bitterness. 3. God will manifest the innocency of the innocent. The same providence is for good to some, and for hurt to others. And it will answer the purposes which God intends.