From the following FAA website link, here’s the official definition of what an FAA 333 Exemption for a commercial UAV business is in the United States National Air Space (NAS):
By law, any aircraft operation in the national airspace requires a certificated and registered aircraft, a licensed pilot, and operational approval. Per Section 333 of theFAA Modernization and Reform Act of 2012 (FMRA) grants the Secretary of Transportation the authority to determine whether an airworthiness certificate is required for a UAS/UAV to operate safely in. This authority is being leveraged to grant case-by-case authorization for certain unmanned aircraft to perform commercial operations prior to the finalization of the Small UAS Rule, which will be the primary method for authorizing small UAS operations once it is complete. The Section 333 Exemption process provides operators who wish to pursue safe and legal entry into the NAS a competitive advantage in the UAS marketplace, thus discouraging illegal operations and improving safety. It is anticipated that this activity will result in significant economic benefits, and the FAA Administrator has identified this as a high priority project to address demand for civil operation of UAS for commercial purposes.
Obtaining the required liability and hull insurance to conform with the requirements of a private or governmental project sought by a commercial firm is up to that firm to qualify and maintain the insurance coverage.