What this checks

Each hop's status code and Location header, followed one at a time (up to 10 redirects).
Redirect loops and chains that are longer than necessary.
Temporary redirects (302, 303, 307) where a permanent one (301, 308) may be intended.
Whether HTTP is upgraded to HTTPS, and whether any hop falls back from HTTPS to HTTP.
Whether the chain ends on a working page, a missing page (404/410) or a server error (5xx).

Reading the status codes

301 Moved Permanently / 308 Permanent Redirect: The content has moved for good. Search engines generally index the destination instead. 308 also keeps the request method (e.g. POST stays POST).
302 Found / 307 Temporary Redirect / 303 See Other: The move is temporary, so search engines may keep showing the original URL. Correct for login pages, short campaigns or maintenance, but a common mistake after a permanent site move.
404 Not Found / 410 Gone: The page does not exist. Fine for content you removed on purpose (410 says it is permanent), but a redirect that lands here throws away the visitors and links it was meant to keep.
5xx server errors: The server failed to answer. Persistent errors stop visitors and reduce how often a site is crawled.

Chains after a migration: update old rules so every legacy URL points directly at its final destination, and update internal links to use the final URLs.
Loops: usually two rules undoing each other (HTTP↔HTTPS or www↔non-www), often one in the CMS and one at the CDN or server. Keep the rule in one place.
HTTP still served: add a single 301 from http:// to https:// at the server or CDN.

Studio requests the URL once, from a server in India, without cookies or JavaScript. Redirects based on login state, country, device or JavaScript (window.location) and meta-refresh tags are not followed.
Only public web addresses on ports 80 and 443 can be checked; private network addresses are refused.
A clean redirect chain does not mean a page is indexed or ranks; only the search engine can tell you that.