A diary the browsers insisted on
Every HTTPS site needs a TLS certificate from a certificate authority. In the early 2010s, a few authorities were compromised or careless and issued certificates for domains like google.com to people who should not have had them. The fix was Certificate Transparency: authorities have to log every certificate they issue in public, append-only logs. Browsers such as Chrome and Safari will not trust most certificates that are not logged.
The side effect is a searchable public record of nearly every certificate issued. For defenders, that record is useful. Attackers read it too, which ATT&CK notes under T1596.003 (searching open technical databases for digital certificates). Same data, used in opposite directions. The standard for the logs themselves is RFC 9162.
After this section you can explain why the logs exist, and why a name in a log is a certificate, not proof that a website is still up.
Certificate Transparency is a diary the authority is required to keep. It is not a warrant, and it is not a list of hosts you are allowed to scan.