The term fully qualified URLs means the use of the complete domain name and path to the particular file.

So, you will use http://www.domain.com/filename.php instead of filename.php.

This is just a brownie points tactic. What we get each time there is a link found to the domain itself is another link pointing at domain.com. It is much better to have the link pointing at domain.com rather than filename.php because it counts as a link to the domain. It may not be much, as it is within the domain itself, but every single link counts. Why waste the points?