Dropbox uses an automatic method of file synchronization. When you place a file into the Dropbox folder the client on your computer immediately and automatically attempts to send that information to the Dropbox server, which in turn immediately and automatically attempts to make the information available to all of the devices you have installed the client on.

Your folder is tied to your account, not to the client software installed on a device. You can only have one main Dropbox folder per account, and a device will only be able to receive the files from your folder if you both install the client and log in to your account. The client will normally only allow one active account at a time to prevent users from circumventing the storage caps placed on the various free and paid accounts.

While Dropbox automatically tries to sync all of the devices you're using, there is only one way that it can do so: the Internet. A device that is not connected to the Internet, or which is has a poor quality or slow connection, won't be able to send or receive files from your folder.

There is an option in the PC, Mac and Linux client's Preferences window that lets you turn on LAN sync. This, however, does not bypass the need to have a constant connection to the Internet when syncing the folder. The LAN sync makes it possible for computers in your home network to directly transfer files, but a connection to the main Dropbox server is still required because only the server knows what folders and files need to be transferred, moved or deleted. The client that you have installed on your computer is effectively brain-dead without the main Dropbox server.