1) function logged_in prints the user navigation links.
2) $this->content['loggedin'] is the array responsible for printing user navigation when user is logged in.
3) if (!isset($this->content['loggedin'])) means if "content['loggedin']" is not(!) set(isset function) then print the value "Welcome and" or anything else.
now what you should do is explained here:
create a file called qa-theme.php and copy it inside your theme directory.
and add this text to it and save:
class qa_html_theme extends qa_html_theme_base
if (!isset($this->content['loggedin'])) echo "welcome and";
$this->output_split(@$this->content['loggedin'], 'qa-logged-in', 'DIV');
any problem: read the article in above link!