When a server returns 403, it's saying it understood exactly what was requested and is refusing to serve it, which is different from a 404 saying the thing simply doesn't exist. The page is there; access to it is being blocked.
On the SEO side, 403s usually trace back to server or hosting configuration rather than anything wrong with the page itself: a firewall rule blocking a search engine's crawler by mistake, permissions set incorrectly on a file or directory, or a security plugin being overly aggressive about what it flags as suspicious traffic. A page that's supposed to be public but returns 403 to Googlebot specifically will quietly drop out of the index over time, since the crawler can't get past the block to see there's anything worth indexing. Checking how a page responds to a real crawler, not just a browser where the visitor is already signed in, is the way to catch this before rankings start slipping.
