This page contains information regarding Star Trek: Picard, and thus may contain spoilers.
A crew manifest (or crew roster, passenger manifest, passenger list, officers manifest, or even drone manifest for Borg ships) was an official list of persons known to be associated with or assigned to a large vehicle or starship. In the case of cargo, that information was kept in a cargo manifest.
The record was usually kept for military or commercial reasons. In early history, the list would be compiled using primitive record keeping and corroboration methods, while more advanced cultures usually used a computer interface to track the persons in question. With the inter-connectivity of database software used on computers, it was usually possible for a user with clearance to obtain and in-depth view of individual personnel files for individuals contained in these lists. (ENT: "The Catwalk")
In 2368, after the long-term memories of the crew of the USS Enterprise-D were temporarily erased by the imposter Kieran MacDuff, Lieutenant commander Geordi La Forge requested a full biographical listing of all personnel responsible for the primary operation of the ship. One was not available, but the computer was able to provide a crew manifest. This, manifest, however, had been altered to incorrectly list MacDuff as a commander serving in the position of executive officer. (TNG: "Conundrum")