Primary verification means verification against the actual book, magazine, ebook, or other work. A primary verifier should ensure that all metadata is correct, and that insofar as possible it is complete. If some data comes from secondary sources, that should be mentioned in the notes. For an anthology or collection, contents including page numbers (when present) should be supplied. If art attributions are determined from signatures (as opposed to explicit credits) or deduced from style that should be mentioned in the notes.
If adding data to a publication primary verified by someone else, you should notify the original verifier on his or her talk page, unless that verifier has indicated otherwise.
If you are changing substantive data (not changing a blank to a non-blank field), it is usually a good idea to ask the verifier in advance.
Primary (Transient) verification should be to the same standards as Primary, but serves notice that the verifier no longer has, or may soon no longer have, access to the work to answer queries. In some cases it is also used as a second verification when a different editor has already done a primary verification.
Primary2, Primary3, Primary4, and Primary5 provide a place for additional people to mark themselves as having done a Primary verification for a publication.