The Libraries API module is a Drupal plugin that connects other Drupal modules to a repository of user-defined libraries that can be downloaded and installed into a folder located at sites/all/libraries or sites/name.of.site/libraries. It allows Drupal modules to draw on files that are not necessarily Drupal modules themselves.
The Libraries API module can be found on their project page on the Drupal site, at http://drupal.org/project/libraries.
Any module that requires the Libraries API as a dependency will also require a 'libraries' folder to be created in the same part of the Drupal directory structure as the Libraries module is found, and a dependent library to be placed in that folder. For example, if the folder containing the Libraries module is found at http://path.to.drupal/sites/all/modules/libraries, then you will need to create a folder called http://path.to.drupal/sites/all/libraries, and place any dependent libraries in there.
Please check the Libraries module's page on drupal.org for more information.