It selects a field in a record of a table. For example if we use a database call to obtain your user record in the Using Moodle course and copy it to the variable $user, then $user->firstname would be Jeremy, $user->lastname would be Welch, etc.
What Zig's written is indeed correct in practical terms most of the time in Moodle.
To be slightly more correct with the terminology though (which may help reading the PHP documentation), $user is an object, and firstame and lastname are properties of that object.