Here is how the Nonprofit Association of Oregon describes it:
Fiscal Sponsorship is an agreement through which a project or organization without tax exempt status partners with an existing tax-exempt organization in order to receive donations and grants. Any nonprofit that the IRS recognizes as exempt under section 501(c)(3) can be a fiscal sponsor. If you are already working closely with a 501(c)(3) organization, you may want to consider asking them to be your organization’s fiscal sponsor. It is important for sponsoree organizations to find a fiscal sponsor that have a similar mission or area of interest, as the fiscally sponsored program is technically a “program” of the fiscal sponsor.
Funds earmarked for the project must be properly controlled and overseen by the fiscal sponsor: they must have the capacity to properly steward the funds, have mission alignment, and a willingness to maintain good communication with the project. It should also be noted that the fiscal sponsor will usually take an administrative fee (typically between 7% and 10% of the sponsored organization’s funds) to cover the costs of administering the sponsored organization’s financial reporting and banking fees.