Cupping is a form of treatment often used alongside acupuncture as part of Traditional Chinese Medicine, as well as being widespread across traditional cultures in Asia, the Middle East and North Africa. It involves first of all applying a massage oil or other suitable lubricant to the part of the body to be treated and then a special cup in which the pressure has been temporarily lowered, either by briefly introducing a flame inside the cup (the traditional method) or with modern cupping devices using a suction pump. It is a little like reverse massage - rather than someone applying pressure to your body, they are reducing the pressure. The immediate effect is that the tissue on which the cup is placed is drawn up into the cup.
If you've not seen it before, it can look a little alarming, but actually it just feels slightly tight and not at all painful - in fact it is sometimes a useful form of treatment for people who might benefit from acupuncture but whose severe needle phobia puts them off. Once the cups are removed, a circular mark will remain on the skin, perhaps for a few days in some cases, which may be inconvenient if you are a fashion model for instance.
One of the most immediate benefits of cupping is that it stretches the tissue under the cup, which makes it a useful treatment for problems involving overly tense muscles. A recent meta-analysis of research into cupping for neck pain, for example, showed significant reduction in pain and corresponding improvement in function (i.e. the ability to turn your head); unwelcome side effects were infrequent, mild and temporary.* Since a lot of neck pain is at least partly due to muscle tension in the neck and shoulders, that cupping should be helpful is not surprising.
Another effect of cupping is to increase blood flow through the area being cupped and its surroundings - often the area will flush red because of this. Again this helps with tight muscles and facilitates tissue healing, which makes it useful in the treatment of ligaments and tendons, which tend to heal slowly because of their limited blood supply.
* Is Cupping Therapy Effective in Patients with Neck Pain? A Systematic Review and Meta-Analysis MJ Open. 2018 Nov 5;8(11):e021070.