Fiscally-sponsored organizations are new or existing organizations that do not have official 501(c)(3) nonprofit status. To apply for and receive grants, these small organizations must use an existing nonprofit organization as a sponsor. The fiscal sponsor will receive funding on behalf of the smaller organization and then transfer the received funds to the organization. The smaller, sponsored organization remains a separate entity and maintains all control over its finances and activities. In contrast, a parent organization has financial and administrative control over any of its programs or departments.
For more information, see this related question:
How do I fill out the Data Profile as a fiscally-sponsored organization?