Dropbox is a web-based file hosting service with desktop clients for all three major operating systems and for Android, iOS, and Blackberry mobile devices. It creates a special folder on machines it is installed on, which synchronizes any files saved in that folder with Dropbox's servers. Any other machine attached to the user's accounts will then have the same changes uploaded to their dropbox folder. Files can also be downloaded and viewed through Dropbox's web interface from any computer with an internet connection.
In addition to syncing computers, Dropbox can also be used for collaboration. Shared folders can be set up between Dropbox users, and any files changed in the shared folder will be changed for everyone who has joined that folder.
Questions about Dropbox at Web Applications should be primarily about the Web interface of the service.