[FlyingDutchman]

• 1st line: when '$loggedinusers' is called from a template, it will show the template 'forumhome_loggedinusers' at that place.
  
• 2nd line(s): It checks if your a user (actually checks if you are NOT userid 0 - != means 'not equal to'), and if so it will assign your username (which is stored in $bbuserinfo['username']) to $username.
  
• 3rd line: Same principe as 1st.
  
• 4th line: You're right about the if-else statement stuff .
  
• 5th line: It basicly assigns a string of nothing between the "s is nothing. It's because if you would open it and the userid IS EQUAL TO 0, then it would just show '$welcometext' on your page instead of nothing (because it doesn't 'know' the variable).
  
• 6th line(s): you assign these both, because they're both for a other variable, you'll need a new eval-line for every variable you want to assign a template to.

I've tried to explain it in easy language - I hope I helped you with this...
I guess you are dutch, but i'm not sure, so if you still need help, then I can also explain in dutch if you want