Your local auth services are configured to use LDAP as a source, whatever your local auth mechanism is checks credentials, and then you’re auth’d or not. Some distros have easy to use interfaces to configure this, some don’t, but mostly it’s just configuring pam.d (for Linux), and a caching daemon of some sort to keep locally cached copies of the shadow info so you can auth when the LDAP server can’t be contacted (if you’ve previously authenticated once). You can set up many different authentication sources and backends as well, and set their preferences, restrictions, options…etc.