Basically there are two types of quote in that string. The first quote is a single quote. This quote is used by the mysql statement to determin a string. This means that $HTTP_POST_VARS['title'] will be entered into the database as a string.
The second type are the double quotes. In the statment above they are used by the php statement. These quotes are used to break out of the mysql statement.
For example. If you where to do this
$word = "test";
print "this is a " . $word;
when run you would get:-
this is a test
printed on the screan.
The final section are the full stops. In php these are used to concatenate, or join, string together. all these are used for in this statement is to make the statement appear on multipul lines.
You could rewrite the statment to make it easier.
$insertQuery = "INSERT INTO articles (title,tagline,section,thearticle) VALUES ('".$HTTP_POST_VARS['title']."', '".$HTTP_POST_VARS['tagline']."', " . $HTTP_POST_VARS['section'].", '".$HTTP_POST_VARS['thearticle']."')";
that will put it on one line.
you could also do this
$insertQuery = "INSERT INTO articles (title,tagline,section,thearticle) VALUES ('$HTTP_POST_VARS[title]', '$HTTP_POST_VARS[tagline]', $HTTP_POST_VARS[section], '$HTTP_POST_VARS[thearticle]')";
This statement will keep everything inside the mysql.
Hope this is helpfull. If not then i will try again.