Burn-in video is a chargeable option when you can "burn in" your captions literally onto the video itself.
You will receive an email when the burn-in video is rendered. Longer, high resolution videos take longer than shorter, lower resolution videos.
If you don't receive an email with a download link to your burn-in video, it is probably because you have unsubscribed from Simon Says emails. In that case, go to your profile page and check your account history. There will be a download link available there. (The download link expires in a few days.)
To learn more about burn-in videos, see here.