Videos are advertisements you can watch in Egg, Inc. They appear in two different scenarios but are not always available to watch.
You can get a notification that a video is ready to be watched on the right side of the screen. If you click the notification, you will be offered either a bonus of Bocks or Golden Eggs. You may then watch the video or decline watching the video, not earning the reward. If there are no ads available (i.e. not being on a connection), the notification will appear but hitting the WATCH button will just decline it.
Drones are paused while a video is playing but they are not paused while you are on the confirmation screen. Therefore if you see a drone appear right after you click the video notification, you should quickly click "Yes" to watch the video and then quickly hunt the drone after the video finishes.
If the option to watch the video is available while your multiplier is still going, watching the video will only reset the timer to its full amount--it will not add the hours to your existing timer.