Add a file to your Dropbox folder, and it will be automatically synchronized across all of your computers. It is available for Windows, Mac, and Linux. There are also apps for Blackberry, Android, and iOS.
If your question is about the PC or Mac app, it may already have an answer at Super User.
If your question is about the Android app, it may already have an answer at Android Enthusiasts.
You can also access all of your files from the Dropbox website, as well as see activity logs and restore files from previous versions (up to 30 days). The free version offers 2GB of storage (at this time) but you can increase this value by referring other people to the service or paying for more storage.
Files and directories can also be shared with other Dropbox users, as well as made public.
There are many apps built to take advantage of the service that Dropbox provides.