What it is
An SSL certificate proves a server is who it claims to be, and is what lets a site serve HTTPS. Certificates are issued by Certificate Authorities, who are meant to verify the holder's identity before signing one. The chain shows every certificate from the site's own up to a root the browser already trusts.
Why it matters
A certificate is public by design, so it doubles as a record: who issued it, when it expires, which organisation it was issued to, and often a list of other hostnames covered by the same cert. That last part regularly turns up subdomains and sister sites nobody advertised.