Leviticus 23:29

For whatsoever soul it be that shall not be afflicted in that same day, he shall be cut off from among his people.

The verse belongs to the Day of Atonement on the tenth day of the seventh month, when the people gathered at the sanctuary to seek pardon while the high priest served in the most holy place.
To afflict the soul means to humble oneself before God, remembering sins, repenting and confessing them so they could be atoned for and blotted out, setting the day apart from ordinary business for solemn humility with prayer, fasting, and deep searching of heart.
Whoever refused that humbling on that same day was to be cut off from among Israel, for the preparation was individual, each searching his own heart and confessing his own sins to seek pardon rather than dwelling on the faults of others.
The same affliction of soul is required now in the antitypical Day of Atonement, while Christ ministers in the heavenly sanctuary and each person's case comes to judgment.
During probation each person must sorrow for sin, truly repent, confess, and humble the heart before God, trusting in the efficacy of Christ's atoning sacrifice to remain in the book of life, accepting His justifying grace and the Holy Spirit's sanctifying work that gives a new nature in holiness and Christ's righteousness.

Original Day of Atonement

The command belongs to the Day of Atonement, kept on the tenth day of the seventh month. On that day the people were to gather at the sanctuary and seek pardon while the high priest ministered in the most holy place. To afflict the soul meant to humble oneself before God, to remember sins, to repent, and to confess sin so that sin could be atoned for and blotted out. That afflicting of the soul was a solemn duty, a humbling of the heart before God in preparation for the great conflict.

The day was to be set apart from ordinary business and spent in solemn humility before God, with prayer, fasting, and deep searching of heart. The required response included confessing and forsaking sin and putting away wrongs between fellow believers, under divine examination in preparation to meet God's standard. Reverence and careful attention to every part of the service were required, impressing God's holiness and abhorrence of sin and the pollution that comes from contact with sin, and showing the seriousness of the day.

Whoever did not humble and afflict himself on that same day was to be cut off from among the people, cut off from Israel. The warning that failure to humble oneself brought cutting off shows how serious the day was. The preparation was individual, with each person examined separately, searching his own heart, confessing sin, and seeking pardon for himself. The lesson is to confess one's own sins and humble one's own heart before God rather than focus on the confessions or faults of others. Afflicting the soul means humbling oneself before God rather than striving for the highest place and causing strife and discord.

Present Antitypical Application

The ancient day prefigures the present antitypical Day of Atonement in heaven, when Christ ministers in the heavenly sanctuary and each person's case comes in turn to judgment. The type required remembering and repenting of sins with humbling of self, and neglect brought separation from the people, so the antitype calls for deep repentance, confession, earnest repentance and careful reverence. Those who would receive the benefits of Christ's mediation must understand His work as High Priest and fulfill the duties required of God's people, gathering in spirit to seek pardon while He serves in the most holy place.

The same affliction of soul is required now, for during probation each person must sorrow for sin, truly repent, confess sins, and humble the heart before God. This preparation is individual, with each person examined separately, and only those who so repent will have their sins atoned for and blotted out and their names retained in the book of life. Such humbling is to be done in trust in the efficacy of Christ's atoning sacrifice, showing the seriousness of the day. Seeking pardon now includes accepting Christ's justifying grace and the Holy Spirit's sanctifying work, which gives a new nature and renews the person in holiness and Christ's righteousness.

During this antitypical period those serving in sacred work are to be holy, giving reverence and careful attention to every part of the service and guarding themselves from contamination. The afflicting of the soul remains a solemn duty, a time to confess sins, humble the heart before God, and get ready for the great conflict. Raising contentions and speculative differences among believers at such a time works against that required soul-affliction and leaves the people confused.