https://futurism.com/neoscope/why-people-get-sick-in-winter

Danner, C. (2022, January 14). Seriously, Upgrade Your Face Mask. Intelligencer. https://nymag.com/intelligencer/article/why-you-should-upgrade-your-face-mask-to-an-n95.html

https://www.popularmechanics.com/science/health/a35383193/n95-vs-kn95-mask-differences/

ECDC. (2021, March 8). We have cross-checked all the latest research on #FaceMasks use during the pandemic. Our position has not changed. Wear it to help slow down the spread of #COVID19! Combine it with #HandHygiene, #CoughEtiquette & #PhysicalDistancing. Be smart. Stay safe. Care about others. Https://t.co/t4AZcJVzld [Tweet]. @ECDC_EU. https://twitter.com/ECDC_EU/status/1368989564321341444

(((Howard Forman))) on Twitter. (n.d.). Twitter. Retrieved 16 August 2021, from https://twitter.com/thehowie/status/1408430486955888642

ReconfigBehSci. (2021, July 26). RT @thehowie: Concerning thread. But this point... 2.14% of asymptomatic people in SF may be infected (vs. 0.1% earlier) is key. WAY too… [Tweet]. @SciBeh. https://twitter.com/SciBeh/status/1419701997582700544

Craig, S., Ames, M. E., Feldman, S., & Pepler, D. J. (2021). Adherance to Public Health Measures in Adolescents versus Adults duing the COVID-19 Pandemic in Canada. PsyArXiv. https://doi.org/10.31234/osf.io/mxfz7

ReconfigBehSci {@SciBeh}. {2021-03-04] there will be many a wrong analysis as we cycle through the 1 year anniversary and there is nothing to mark this one out as uniquely bad, but what does seem surprising to me in hindsight is the confidence with which people pronounced given that this was a new disease.[Tweet}, Twitter. Retrieved from: twitter.com/SciBeh/status/1367531205198049285

Grover, Natalie. ‘Should Primary Schoolchildren Be Made to Wear Masks?’ The Guardian, 2 March 2021, sec. Education. https://www.theguardian.com/education/2021/mar/02/should-primary-schoolchildren-be-made-to-wear-masks.

WearingisCaring {@WearingisCaring} (2020) How can you safely take off your mask? Simply follow these four easy steps to prevent catching the virus! Twitter. Retrieved from: https://twitter.com/WearingisCaring/status/1295707116880134145

Take away: Though not a guarantee of health, wearing masks reduces the number of respiratory infections compared to no/inconsistent mask wearing.

The claim: Masks are protective against clinical respiratory illness.

The evidence: The authors performed a meta-analysis of random controlled trials and observational studies examining mask use in health care workers. The results showed that wearing masks resulted in fewer infections compared to people without masks. These results agree with other publications (1, 2). One pre-print article which performed meta-analysis showed inconclusive results concerning the effectiveness of masks (3). Based on these meta-analyses, mask wearing results in fewer respiratory infections, though it will not prevent all infections when used as the sole protective measure.

Sources:

1) https://pubmed.ncbi.nlm.nih.gov/32497510/

2) https://pubmed.ncbi.nlm.nih.gov/27632416/

3) https://www.medrxiv.org/content/10.1101/2020.03.30.20047217v2

Gandhi. M., Beyer. C., Goosby. E., (2020). Masks Do More Than Protect Others During COVID-19: Reducing the Inoculum of SARS-CoV-2 to Protect the Wearer. SpringerLink. Retrieved from: https://link.springer.com/article/10.1007/s11606-020-06067-8

Liebst, Lasse Suonperä, and Marie Rosenkrantz Lindegaard. ‘Face-Touching as a Possible Correlate of Mask-Wearing: A Video Observational Study of Public Place Behavior during the COVID-19 Pandemic’. Preprint. PsyArXiv, 22 August 2020. https://doi.org/10.31234/osf.io/u6wcp.

‘Coronavirus Cases Surge as France Goes “Wrong Way”’. BBC News, 11 August 2020, sec. Europe. https://www.bbc.com/news/world-europe-53745481.

AP NEWS. ‘Health Officials Are Quitting or Getting Fired amid Outbreak’, 10 August 2020. https://apnews.com/8ea3b3669bccf8a637b81f8261f1cd78.

It sounds like it's recommended because a significant portion of people with coronavirus are asymptomatic or pre-symptomatic, and the virus can spread through speaking, coughing or sneezing.

There's no "proof" that these work, but there's a hope that it helps along with hand washing and a distance of six feet.