Killswitch is a multi-platform app that runs on your phone and computer(s), allowing you to remotely lock or shut down all your devices with the touch of a button.
The app for your phone/tablet is the remote control, and the app running on your computer (or other device) is a background process that listens for the remote signal. You can have an infinite number of remotes and listeners tied to the same account, the only limitation (by design) is that they all react to the same signal. Eg. If you want to lock computers individually, you need multiple accounts and multiple remotes.
While your killswitch is active, any computers bound to the system will keep locking until you turn the killswitch off with your remote. This is the intended functionality and offers you some degree of security even if your system password is known to someone else.