Although Mendeley Desktop and Mendeley Web look similar, there are some feature differences.
Mendeley Desktop is best for storing, editing, and viewing PDFs on your computer and automatically creating reference data from PDFs.
Mendeley Web gives you access to your saved research on the go and allows you to import documents found while searching the web or online databases.
The Watched Folders feature for Mendeley Desktop is invaluable. PDF files that you save to a folder will be automatically added to your Mendeley Desktop library.
Check out Zotero and EndNote as alternatives, or see what other citation managers can do.
To add PDFs/references to the Mendeley Desktop:
Mendeley Minute: Importing Documents into your Library (2:04)