From version 5.5 of PHP, the mysql_ functions have been deprecated. http://php.net/manual/en/migration55.deprecated.php
In future versions these functions will be removed and older versions of phpList will stop working.
To avoid this from happening, you will need to change your config file and find the line:
$database_module = "mysql.inc";
and change it to
$database_module = "mysqli.inc";
The change is very small, so if you do not see it, it is a lower-case letter i before the full stop.
If you do not have this line in your config file, then you do not need to do anything, and you can upgrade to the latest version of phpList.
This change applies to phpList version 3.0.7 and up. If you run a version prior to 3.0.7 you will need to upgrade to the latest version of phpList first.