There are some background video modules available (see these video modules in the marketplace).
However, personally I’d make my own custom Module for this. Basically, it can just be a kind of VideoContainer - you can expose a couple of fields (like embed codes, for different sizes) and display the videos either with a <video> tag, or an <iframe> if you want to use a third-party embed from YouTube. Note that you can’t use video sources like you can for images, so if you want a different video for mobile devices, you may have to use a little JavaScript to handle dynamically determining the video file to use .