The process makes file to read via http (not https), it’s just a nonce ( some random characters). Once their server reads that file, using the domain (and not the ip) and compares with what is expected, this shows you own the domain , and they give you a new ssl cert, modifying your server’s https configuration file (usually). And deletes the file it made .
This is early days; I have a feeling in a few short years there will be ownership and simplicity of distributed services and whatever evolves from them.