An EUA allows use of unapproved medical products (or unapproved uses of approved medical products) to diagnose, treat, or prevent serious or life-threatening diseases or conditions caused by threat agents, such as Covid-19, in response to a declared public health emergency for which there are no adequate, approved, and available alternatives.

https://www.nejm.org/doi/full/10.1056/NEJMp2031373

Does this apply to vaccines?

In addition to the legal uncertainty, some commentators have raised ethical questions about mandating a vaccine that is subject to EUA. The EUA authority requires less evidence of safety and efficacy compared to full FDA approval (usually based on the duration of safety and efficacy data available). Specifically, an EUA is permitted during a public health emergency, if the FDA determines that it is reasonable to believe the vaccine “may treat or prevent” the disease, the known and potential benefits outweigh the known and potential risks, and no approved adequate available alternative exists (emphasis added).

https://www.kff.org/coronavirus-covid-19/issu...-mandates/