Most sites prove their identity to you; a few also demand proof of yours. Government, banking, and corporate systems sometimes require a client certificate, stored on your machine or a smart card, during the TLS handshake. This error means the certificate your browser offered was rejected: expired, issued for a different purpose, not the one the server expects, or impossible to read (a smart card problem is the classic).
certmgr.msc → Personal → Certificates shows your client certificates. The right one must be unexpired and intended for client authentication. An expired certificate must be renewed by its issuer; there is no local workaround.If the correct, unexpired certificate is selected and the server still refuses, the server side has your certificate's record wrong (not yet enrolled, revoked, or mapped to another account). That is fixed by the organization that issued it; bring them the certificate's serial number and the exact error.
Why does only this one site ask me for a certificate? Client certificates are an opt-in, high-assurance login method used by organizations that need strong proof of the user or device. Ordinary websites never request one, so the prompt and this error only appear on those specific systems.
Can I skip the client certificate and log in with a password instead? Only if the organization offers that option. Where a client certificate is required, it is the login; there is no browser setting that substitutes a password for it.