Confidence that an entity possesses a private key associated with a given public key.
Sources:
NIST SP 800-56B Rev. 2
under Assurance of private key possession
Confidence that an entity possesses a private key and its associated key information and that the private key corresponds to a given public key.
Sources:
NIST SP 800-57 Part 1 Rev. 5
under Assurance of (private key) possession