Do you mean amount of posts on the board made since you last visited or the amount of posts you have made since you logged in??
If its the former I don't know what use this would be in the profile??
If it's the former I'm great at these things but I would guess you could do something like:
Firstly - add a new column (INT) to {db_prefix}members called PrevLog. Can do this with a db file or phpmyadmin
In loginout.php go to :
$request = mysql_query("DELETE FROM {$db_prefix}log_online WHERE identity='$ID_MEMBER'") or database_error(__FILE__, __LINE__);
and add this:
$timeout=time();
$result = mysql_query("UPDATE {$db_prefix}members SET PrevLogin='$timeout WHERE memberName='$username'") or database_error(__FILE__, __LINE__);
Then, whereever you want to add the total amount of new posts since your last visit:
$request=mysql_query("SELECT PrevLogin FROM {$db_prefix}members WHERE memberName='$username'") or database_error(__FILE__, __LINE__);
$timeon = mysql_fetch_array($request);
$request=mysql_query("SELECT subject FROM {$db_prefix}messages WHERE posterTIME>$timeon[0]") or database_error(__FILE__, __LINE__);
$numnew=mysql_num_rows($request);
Then you can print the variable $numnew whereever you want to display it (profile, info center - whereever)
I think this should work. I'm not *quite* sure how logging out is handled if you don't logout manually and this depends on the logout function getting called for you - hopefully it does get called

. It will just count all the messages that have been added since you last got logged out.