When a display is in draft mode users who visit the site will not be able to see the display. A display in draft mode will never trigger or appear.
If a display is switched to live mode it will be possible to trigger and may appear to visitors if settings and targeting allow.
The draft / live switch is your master control to decide what appears on your site and what doesn't. It can never be activated automatically. For example if you were to set a schedule for your display under 'rules' for the display to begin appearing at a certain date but leave the display in draft mode it will never appear. If you want a display to appear or begin to appear at a certain date / time it must be set to live.