This release introduces quite a few bug fixes; for full list of things that has been fixed/improved in 3.2.4, please take a look at our issue tracker.
For more details on major new features/highlights, please refer to 3.2 release blog post, here's the short list:
You can download the release from SourceForge – select from the civicrm-stable section. The filenames include the 3.2.4 label: civicrm-3.2.4. Make sure you’re downloading correct version: for Drupal or Joomla.
If you are installing CiviCRM 3.2.4 from scratch, refer to the installation guide:
The procedure for upgrading to 3.2.4 is the same as for upgrading to 3.0.x. You can upgrade directly from 2.2.x or 3.0.x or 3.1.x. Instructions: