Dropbox is a cloud based file storage system. After creating an account you can access files through a web browser, a mobile application (e.g. Android, iPhone/iPod/iPad) or simply through a folder in your computer's file system when you install a Dropbox client application (Windows/Mac/Linux). In fact after installing one of the client applications, your files will be synchronised in the background to the cloud store and back down to any other systems you have with the client application running.
This makes Dropbox not only a great way to keep files in sync across multiple computers, but also as an offsite backup. Dropbox also allows you to share sub folders with other users so you can synchronise files not only with yourself, but also colleagues or family members.