This variable is normally set by the MediaWiki installer, but may need to be adjusted after your LocalSettings.php is generated.
The base URL of the server, including protocol but without the trailing slash and without the subdirectory if any (e.g., https://www.mediawiki.org).
Since version 1.18.0 MediaWiki also supports setting $wgServer to a protocol-relative URL (e.g., //www.mediawiki.org).
This is used for supporting both HTTP and HTTPS with the same caches by using links that work under both protocols. When doing this, $wgCanonicalServer can be used to set the full URL including protocol that will be used in locations such as emails that do not support protocol relative URLs.
If the URL starts with https://, MediaWiki will assume that your wiki prefers the HTTPS protocol or supports it exclusively.
The setting to this configuration parameters is used when producing fully-qualified URLs pointing to the wiki, for instance:
HTTP redirects on edit and to canonical URL spellings
links to articles from RSS/Atom feeds
links to articles from notification emails
Please make sure that $wgServer is set to your actual base URL and not to http://localhost (unless you actually want to only access MediaWiki through your localhost). Otherwise links will not work.
MediaWiki formerly tried to autodetect the name of the server, however this was vulnerable to cache poisoning attacks, and informally deprecated in 1.18.
It was fully removed in MediaWiki 1.34.