Sitemap and robots.txt check
The two files every crawler asks for first, and the two most often quietly wrong.
Why the two are checked together
They are one system, not two files. robots.txt is where a sitemap is announced, and a sitemap nobody is told about is a file nobody fetches. Checking either on its own misses the failure that actually costs traffic: a perfectly correct sitemap that no robots.txt points at.
Both are plain text at a fixed address, which is why this takes a second and why there is no excuse for either being wrong. They are also the first two things a crawler asks for, so a mistake here is a mistake at the very front of the queue.
The line that takes a site off Google
Disallow: / under User-agent: * tells every crawler to stay out of the entire site. It is the correct setting on a staging server and a catastrophe on a live one, and it travels between the two more often than anyone would like — usually in a copied folder, occasionally in a restored backup.
Nothing visibly breaks when it happens. The site loads, the pages work, and the traffic quietly stops over the following fortnight. This check is looking for exactly that, first, before anything else.
What a good sitemap contains
Only URLs on its own hostname, only ones that return 200, and only the canonical version of each. A sitemap listing http:// addresses on an https site invites a redirect on every page a crawler visits, which wastes the crawl budget you have on work that produces nothing.
Dates help. A lastmod that is honest tells a crawler what to re-read and what to leave alone; one that is set to today on every page tells it nothing and is eventually ignored.
Size matters less than people fear. A sitemap may hold fifty thousand URLs, and above that you use an index file that points at several — which this check follows and reports on.
What this does not do
It samples three URLs rather than crawling all of them. That is enough to tell you whether the file describes a real site or a stale one, without turning a button press here into hundreds of requests against your server.
It also does not judge which pages should be in the sitemap. A thin tag archive and a good article look identical to a validator; deciding what deserves to be indexed is editorial work, and no tool does it for you.