A signer acts in a representative capacity when signing on behalf of another person or legal entity rather than only in an individual capacity.
Examples may include:
a president signing for a corporation
a manager signing for an LLC
a partner signing for a partnership
a trustee signing for a trust
an attorney-in-fact signing under a power of attorney
another authorized representative signing for an organization
The notarial certificate may need to reflect that representative capacity when the document and applicable law call for it.
The Uniform Law Commission's Revised Uniform Law on Notarial Acts defines an acknowledgment to include a declaration that, when a record is signed in a representative capacity, the individual signed with proper authority.
That model language is useful for understanding the issue, but RULONA is not one federal law governing every U.S. notary. The commissioned online notary must follow the law applicable to the notary's own commission.