The desktop version of Mendeley has some advanced features, including storing, indexing and importing PDFs so that you can use it to organise your collection of documents. There are currently two desktop versions; Mendeley Desktop and the new Mendeley Reference Manager.
In order to use Mendeley Desktop you need to register with Mendeley.
Mendeley also provides a Web Importer tool which allows you to import citations, and sometimes the full text article, directly from your browser in to your library.
To install the plugin from the Mendeley app click Tools >> Install Web Importer.