What the domain report checks
A domain is not one thing. It is a registration held at a registry, a set of DNS records served by nameservers, one or more servers that answer on the IP addresses those records point to, and usually a mail setup that lives somewhere else entirely. Problems tend to appear in the gaps between those layers, so the report looks at all of them in a single pass.
The registration section comes from RDAP, the structured successor to WHOIS: registrar, creation, update and expiry dates, status codes, nameservers and DNSSEC state. The DNS section queries public recursive resolvers for A, AAAA, NS, MX, TXT, CAA and SOA records. The mail section reads MX, SPF and DMARC. The hosting section maps each IP address to its network owner. The web section makes one HTTPS request and records redirects, the response status and the certificate the server presented.