A certificate encodes an identity, like a name of a website.
A certificate authority issuing such a certificate vouches that the entity to which the certificate is given (more precisely: the entity owning the private key associated with this specific certificate) is indeed having that identity, that is owning this website.
The validation is to prove the entity is owning that website by, typically, either putting some specific content at specific location on the website or altering some DNS records in the zone. Both operations showing that the entity controls the name at the DNS level (or HTTP level) and hence the certificate can be delivered.
If you want to dig deeper, based on your question, you need to thorougly understand that each of the following job is separate from all others, except that a given entity can do more than one or even all of them:
- a domain name registrar, where you register your domain name
- a DNS provider, controlling the content of the zone
- a webhosting company, providing a listening webserver on names in the zone
- an email company, providing services to receive or emit emails using this domain
- a certificate authority, issuing certificates for names in the zone.