Auspices means the support, sponsorship, or protection of an organization or person, especially one with authority or influence. When something happens under the auspices of a group, that group is officially backing it or making it possible.

If your school holds a science fair under the auspices of the local university, the university is sponsoring and supporting the event, lending its name and resources to make it happen. When a charity fundraiser operates under the auspices of a national organization, that larger group is overseeing and legitimizing the effort.

You'll often see this word in formal contexts: a concert performed under the auspices of the city's arts council, or a research project conducted under the auspices of a major hospital. The phrase suggests not just permission, but active support and the credibility that comes from having a respected organization behind you.