The PC application puts an easy to access folder on your computer than links directly to the Cloud. You can easily add sub-folders to your Dropbox folder, which makes it easy to organize your space. From your desktop you can simply drag files into this folder and it will automatically sync the files to the Cloud and your devices. Mobile devices have the ability to send files to your Dropbox as well; while looking at pictures on my Smartphone, I can send them to Dropbox without opening the app by opting to Share the file to my Dropbox folder. Depending on your settings, the actual files are sent to all of your devices, so that even if you aren't on the network, you can open the files and use them.
Dropbox allows you to share files with other users by changing the settings of that folder to public, shared or private. Public files are available to anyone who has the time to figure out your username. Shared files can be worked on by those you invite to access your folder. Multiple people can work on a given document at once, and Dropbox will save the different versions in your folder under slightly different names. Photos you send to your Dropbox Photo file can be viewed on an on-line gallery with a sharable link you can give to friends and family. Finally, Private files are only accessible by you.
I have the Dropbox app on my Smartphone (Android-based) and iPad, and I have application loaded on my home and work PC. I love that I can access files anywhere I have wi-fi or a 3G signal with my mobile devices. I find it useful when I work on a document from home and want to continue to use it at work. Instead of trying to find a flash drive (with enough free space), I send the file to Dropbox and open it back up at work. I've used it to share music files I purchased on my Smartphone and wanted to have on my desktop (before I discovered Amazon Cloud), and rather extensively for documents of all types (Word, PDF, PPT., etc). I was also successful in sending a short video I made in PuppetPals on the iPad, which I exported as a Quicktime and then sent to Dropbox, where I was able to pick it up on my work PC (which isn't the one my iPad is synced with). Overall, I find that Dropbox has been one of the most useful app I have downloaded and it should be one of the first few apps you download for your devices.