The practice is fairly popular in Russia but is also practiced in other countries, although the Russian variant seems to be the most extreme. Broader general awareness of the practice originated via a truly hair-raising YouTube video (seriously, try to watch it without wincing in disbelieving horror at least once) in which the arguable guru of the practice, Lena Fokina, whirls a baby around in the air like a pair of nunchaku, coming within a hair's breadth of dropping it several times.
The purported claims are that it makes infants "more open" (whatever that may mean), more sociable, and more relaxed;  another practitioner claims that babies who undergo this therapy "are early readers, singers, talkers, swimmers". These claims are unproven, and no research has been performed on this practice. Not only is it too crazy to take seriously, but research would also be unethical due to the likely dangers and lack of informed consent. Consider being picked up and swung around in all directions. Would this make you happy? Relaxed? More sociable? Improve your reading skills? Or would it make you dizzy, sick, and fairly annoyed at the person who was doing the swinging?
Unlike some other quack nonsense, this particular breed has some very clear and direct dangers:
- Death, we repeat, DEATH from shaken baby syndrome. SBS isn't necessarily fatal; the lucky babies end up blind or with a motor and/or cognitive impairment.
- Serious trauma (and again, possible DEATH) from hitting something (furniture, floor, etc). Consider doing this 20 hours a week for a living; do you think it's possible that at some point you slip up, no matter how careful you are? There is a very low margin for error here.
- Dislocated joints. Unlike adults, a young child's elbow can become quite easily dislocated (this is called a Nursemaid's elbow).