Dropbox doesn't require much user interaction to sync files. If you drop a file in the Dropbox folder on any computer linked to your account that file becomes available on all your computers and devices. The computers receiving the data do not have to take any action in order to have the folder updated, and no notification appears when a new file is uploaded.
This means that you can use Dropbox to trigger actions on a computer that you are not currently using. The most powerful such program is Akira, a program that lets you control a computer remotely via Dropbox via a wide range of text commands.
You can also remotely control a computer using Dropbox with any program that is capable of automatically taking an action when a file appears in a folder. Bittorrent clients are the most popular example of this. Most are capable of automatically beginning a torrent download if a torrent file is placed into a specified folder. This means that you can place the torrent file into your Dropbox folder from a remote computer and have that file begin downloading on your home PC.