The cilice is a chain or strap with small spikes in it. Numeraries and associates wear it around their thigh for 2 hours a day. It has also been described as a wire mesh, with the ends of the wires pointing inward. Sometimes the points are filed down.
The discipline is a cord with knots in it. Once a week numeraries and associates use it to strike themselves.
Jesus invites all Christians to help him carry the cross. It’s true that for most of us there are plenty of crosses in our daily lives, and we don’t need to invent new ones. Nevertheless, it’s a good and longstanding Christian practice to deny ourselves some simple pleasures in order to fortify our will, remind ourselves of the passing nature of this world’s goods, unite ourselves to the sufferings of the Lord in his passion, and to offer atonement for our sins. This is the purpose of the ancient practice of fasting and abstaining from meat, for example.
It’s interesting that many people understand the need to deny themselves sweets and excessive amounts of food and to get up early in the morning, regardless of the weather, to run miles and miles, enduring great physical pain. They will submit to painful operations and medical treatments, even to the point of injecting poisons—for example, chemotherapy and botox—into their bodies. They do all these things to preserve or restore their physical health, or even just their beauty. Yet they recoil at the idea of doing things that cause far less physical discomfort if the motivation is spiritual in nature. These are the people who don’t understand and are horrified at the practice of corporal mortification.
It seems to me that the controversy over the use of these means of mortification arises from the fact that they’re intended to fortify the soul rather than the body, and they don’t involve the use of Spandex® or a membership in a health spa. However, these are traditional means used by many saints in the church’s history, and even if they aren’t used quite so much today, that doesn’t diminish their value.
It’s true that these types of corporal mortifications are not for everyone. In Opus Dei, only numeraries and associates use them and they must ask permission to do so more frequently than prescribed. It is my understanding that supernumeraries are not allowed to use them.
It has been reported that the cilice causes severe pain, and can even draw blood. It seems to me that would depend on how tightly you wear it. It has also been reported that numeraries whip themselves with the discipline to the point where blood splatters the walls. While I’ve never seen either a cilice or a discipline, I find it preposterous to believe that. The best I can tell, this lie is based on a true story about St. Josemaría in which he did use the discipline to the point of drawing quite a bit of blood. But he tried to hide this from others and even forbade his sons and daughters from imitating him in this matter. He believed that his unique role as founder required this sacrifice from him, but not from others.
Like I said, I have never seen either the cilice or the discipline, much less used them, but this answer has been read both by a former numerary who is now opposed to the Work and by a current numerary, and they agree it is accurate.