In Omelas, the happiness of the many depends on the suffering of one innocent child, who is forced to live a loveless life and is hungry, covered in sores, and mired in filth so that the rest of the society can experience joy, beauty, and pleasure. The ritual associated with this child is that of forcing everyone older than a certain age to walk past and see the horrible conditions in which the child lives.
This ritual helps invalidate the calculus of utilitarian pleasure and pain on which this society is built. Utilitarianism defines happiness as the greatest good for the greatest number. However, the fact that everyone knows the price the child pays makes utilitarianism no longer an abstract concept but a concrete experience of another's pain. This ritual, therefore, renders everyone in the society complicit with the neglect of the one child: they know experientially what is going on. Knowing how the one child suffers invalidates the idea that is acceptable for any one person to suffer for the good of the many: the citizens of Omelas know they are guilty of a great wrong, even if they try to rationalize it away.
The only people validated in the story are those who walk away from Omelas to begin a new life elsewhere. They refuse to base their pleasure on the pain of another and so show their integrity.