Vine Reminder monitors all upcoming events that you are responsible of and which have the reminder option active. When the reminder time comes up, it will show you a dialog where you can check the event and decide whether you need more reminders about it:
The Reminder starts automatically when you run Vine. If you want to get reminder messages without first running Vine you need to run Vine Reminder yourself or add a shortcut to it to the Startup folder of Windows so that it starts when Windows starts. Note that when you close Vine, Vine Reminder is not closed and will be still running.
You can turn off Vine reminder by selecting Show Settings from the main Menu and selecting Disable Reminder.