What DNS propagation really is
Nothing is pushed across the internet when you change a DNS record. Your authoritative nameservers start serving the new value immediately. What takes time is that recursive resolvers, the servers your visitors actually ask, keep the old answer until its TTL runs out. Each resolver cached it at a different moment, so each one switches at a different moment.
That is why two people can see two different versions of your site for a while, and why a change with a 300 second TTL settles in minutes while one with an 86400 second TTL can take a day.
How this check works
OrbitProbe sends the same question to ten independent public resolvers: Cloudflare, Google, Quad9, OpenDNS, AdGuard, Yandex, DNS.SB, Verisign, Lumen and CleanBrowsing. Answers are normalised, so the order of records and upper or lower case do not count as a difference, and then grouped. You see how many resolvers returned each distinct answer, and which ones returned no record, said the name does not exist, or could not be reached.
A resolver that failed is shown as failed. It is never counted as agreeing, and the result is only called consistent when every resolver answered and every answer is identical.
What the result does and does not tell you
The result describes these ten resolvers, as seen from our server, at the time shown. It is a good early signal, because these resolvers serve a large share of real users. It is not a measurement of the whole internet, and no tool can give you one: there are millions of resolvers, including the one at every ISP and office.
Most of these resolvers are anycast networks. The node that answered us may not be the node that answers a visitor on another continent, and the two can hold different cached values for a short time.
If the answers disagree
Disagreement shortly after a change is normal. Check the TTL of the old record: that is the longest a well-behaved resolver will keep it. If answers still differ long after the old TTL has passed, query your authoritative nameservers directly. When two of your own nameservers return different values, the zone was not updated everywhere, and that is a fault to fix rather than something to wait out.
For a nameserver move, keep the old zone running and identical until the delegation TTL at the registry, often 48 hours, has passed.