Site certificate
A site certificate is the file behind the padlock in your address bar. It proves that the connection between you and that domain is encrypted, and that the certificate was issued to the domain you are actually on.
Where you see it
Clicking the padlock shows which domain the certificate covers and who issued it. A missing, expired or mismatched certificate produces a browser warning before the page loads.
Why it matters
This is the most misread signal on the web. The padlock means the connection is private, not that the operator is honest - a clone site can obtain a perfectly valid certificate for its own lookalike domain, and most do. Use it for the one thing it settles: check that the name on the certificate is the domain you meant to open, and never type a card number into a page your browser is warning you about.