Others have covered this phenomenon extensively; such is the bright and microscopic nature of Olympics reportage. There are segues and human interest stories to be filed for the interstices of the wall-to-wall coverage.
What are those mysterious circles visible on athlete's bodies? The answer is: cupping hickies/bruises.
What is cupping?
CNN: Olympics in bright red spots: What is cupping?
Believers are convinced!
Cupping Resource: How does Chinese cupping therapy work?
Like most "alternative"/homeopathic practices, cupping offers anecdotal tales and theories for medicinal//performance value. Many are the stories; none are the clinical studies.
Cupping was addressed by skeptics long ago.
Skeptic's Dictionary: Cupping
Here's a newer takedown.
Insolence: What’s the harm? Cupping edition
A call for sanity is inevitably lodged.
The Atlantic: Please, Michael Phelps, Stop Cupping
Make no mistake: if deafness were an Olympic event, the ears upon which such pleas fall would win the gold.
Not only will Phelps continue to cup, but look for the cupping hickies on other athletes. All events; many nations. Trust that the practice will filter through to college and eventually high school athletes. Without the benefit of evidence, the practice offers a mystical advantage that promises adherents a competitive advantage. Who will dare put him herself at a "disadvantage" by not jumping on the band wagon?
The takeaway is that there will always be something. Some untested, evidence-free "edge" that athletes will flock to. Copper bracelets, magnet bracelets, hologram bracelets, aqueous metal-infused necklaces. This month: cupping. An objective observer might hope for some placebo effect. But that's all anyone can hope for.
There are many more links to be perused at one's leisure. If you see a nice one, let me know.