What the MX records say
An MX record names a server that accepts mail for the domain, with a number in front of it called the preference. A sender tries the lowest number first and moves to the next one if that server does not answer. Two records with the same number share the load. The checker lists them in that order and resolves each host name to its IPv4 and IPv6 addresses.
When a domain has no MX record at all, senders fall back to its A or AAAA record and try to deliver there (RFC 5321, section 5.1). That is rarely what anyone wants, since the address behind a bare domain is usually a web server.
Records that break delivery
An MX record has to point at a host name. A record that points at an IP address is invalid. So is one whose host name is a CNAME, which RFC 2181 forbids. Most senders follow it anyway and a few give up, so the domain receives mail from one provider while bouncing it from another. The checker flags both cases, and a host name that does not resolve at all, which can mean a migration left an old server behind.
A null MX, a single record of 0 followed by a dot, says the domain accepts no mail (RFC 7505). It is the right answer for a domain that neither sends nor receives mail, and senders stop trying at once instead of retrying for days. A domain you send from should not have one: replies and bounces need somewhere to go.
Why a sending domain needs working MX
Bounces and replies go back to domains, so a domain you send from has to be able to receive. The domain in the Return-Path collects bounces, the From domain collects replies, and some receivers check whether these domains accept mail before taking a message from them. A sending subdomain with no MX and no A record can look like a made-up domain.
The checker also looks for MTA-STS and TLS-RPT records next to the MX list. Missing them does not stop mail arriving today. With them in place, senders that support MTA-STS refuse to deliver to you without encryption, and TLS-RPT tells them where to report when that fails.