Dropbox uses a combination of software client and web client which provide both access to the files unlike normal file hosts like Rapidshare who provide no way to sync files across computers.
The software client basically uses one source folder on the hard drive where all the files and folders are stored in locally. Uploading files is just a matter of moving files and folders into the Dropbox zone on the computer or by creating and editing files already in that special folder.
When the Dropbox client is running the files and folders will get automatically synced with the online client which keeps the most recent copies of the files and folders including file revisions. The web client of DropBox can be used to download or view files without having to run the software client. The client can also be used to upload new files to the service.
Dropbox currently has a 2 Gigabyte limit for every user which is definitely enough for many purposes. One of the interesting features of Dropbox is being able to share a folder with another person. It pretty much works the same as sharing a folder between different computers.