When you connect securely to a site, you need assurance that you are talking to the real one and not an impostor. A digital certificate, issued by a trusted authority, vouches for a server's identity, and your browser checks it before trusting the connection.
The system rests on a chain of trust: your device trusts a few authorities, which vouch for others, which vouch for individual sites. It works well but depends on those authorities behaving correctly, which is why their mistakes are treated so seriously.