In order to feature an event in the slider on the Events page, it must first be added to the Featured Events nodequeue. Once it is in the NodeQueue, it will be cycled in the slider until you remove it.
To add an event to the NodeQueue, first navigate to the event itself. If you are a Content Editor or an Administrator, you will see a "NodeQueue" tab above the content of the event:
Click the "Nodequeue" tab, and on the screen that follows, click the "Add to Queue" link to add it to the Featured Events Nodequeue:
To manage all nodequeues, select Structure from the top menu, then Nodequeues from the page that follows.