Dropbox is the iOS companion app to the free Dropbox Web service and desktop software. If you have Dropbox set up on your Mac, this app lets you sync, share, and download files and folders from your computer using your iPhone or iPad.
The Dropbox mobile app basically gives you another interface for accessing your Dropbox folder, a local folder that you set up on your Mac. Anything you put in that folder, you can see on your iPhone or iPad. The interface gives you tools to view the file (surprisingly quickly, and without losing quality even with MP3s and video files), open the file in another app (particularly useful on an iPad outfitted with other productivity apps), or share the file (either by e-mailing a link, or by copying a link to your clipboard). You can also "favorite" a file to save it to your device for offline viewing. (Since your Dropbox folder could be as large as 100GB, the app doesn't automatically download all of it.) Dropbox can view a broad range of file types, from common image and text formats to Microsoft Office files and Keynote presentations.
The Dropbox mobile app doesn't do everything--for instance, it would be nice to add and edit files from inside the app--and performance isn't always reliable with large files. That said, Dropbox is an extremely easy and free way to access and share files from your Mac, and if you're already using Dropbox on your Mac, this is a must-download.