PHP Lib is a collection (or 'library') of interfaces, classes and functions that are used by a variety of Islandora modules, most notably the Forms modules. It is used primarily to create pages that convert records in XML formats to a more human-readable version that is also able to be easily manipulated. This is done by a series of PHP files that Drupal includes when loading these pages.
PHP Lib has no dependencies, but also has no functionality as a standalone module.
Objective Forms is part of the Islandora Forms package, downloadable at the Release Notes and Downloads page.
PHP Lib requires no configuration, and functions as soon as it is activated and installed as a Drupal module.