It doesn't. Intro section on Wikipedia [0] already lists five studies that concluded it doesn't work: "Clinical research does not show reiki to be effective as a treatment for any medical condition, including cancer,[4][5] diabetic neuropathy,[6] or anxiety and depression,[7] therefore it should not replace conventional medical treatment. There is no proof of the effectiveness of reiki therapy compared to placebo. Studies reporting positive effects have had methodological flaws.[2]"
[0] https://en.wikipedia.org/w/index.php?title=Reiki&oldid=94822...
[2] Lee, MS; Pittler, MH; Ernst, E (2008). "Effects of reiki in clinical practice: A systematic review of randomised clinical trials". International Journal of Clinical Practice (Systematic Review). 62 (6): 947–54. doi:10.1111/j.1742-1241.2008.01729.x. PMID 18410352. "Most trials suffered from methodological flaws such as small sample size, inadequate study design and poor reporting....In conclusion, the evidence is insufficient to suggest that reiki is an effective treatment for any condition. Therefore the value of reiki remains unproven."
[4] Russell J; Rovere A, eds. (2009). "Reiki". American Cancer Society Complete Guide to Complementary and Alternative Cancer Therapies (2nd ed.). American Cancer Society. pp. 243–45. ISBN 9780944235713.
[5] "Reiki | Complementary and alternative therapy | Cancer Research UK". about-cancer.cancerresearchuk.org. Retrieved 2020-02-12.
[6] Bril, V; England, J; Franklin, GM; Backonja, M; et al. (2011). "Evidence-based guideline: Treatment of painful diabetic neuropathy: Report of the American Academy of Neurology, the American Association of Neuromuscular and Electrodiagnostic Medicine, and the American Academy of Physical Medicine and Rehabilitation" (PDF). Neurology. 76 (20): 1758–65. doi:10.1212/WNL.0b013e3182166ebe. PMC 3100130. PMID 21482920.
[7] Joyce, Janine; Herbison, G Peter (2007-10-17), "Reiki treatment for psychological symptoms", in The Cochrane Collaboration (ed.), Cochrane Database of Systematic Reviews, John Wiley & Sons, Ltd, pp. CD006833, doi:10.1002/14651858.cd006833