To keep your website fast, we only allow pictures to be uploaded to your media library. Video is a totally different beast from images and other website content. Most browsers all handle video a little differently, and serving up all that bandwidth is not what our platform is best used for. That said, your site absolutely has support for video content.
The majority of the time we recommend embedding YouTube videos onto the site. YouTube has a easy-to-use embed code that you can copy/paste right into the post's content. So, first step: find a video service provider you want to use. We suggest using YouTube since it is free, fast, and offers lots of functionality out of the gate. It also is the world's #2 search engine, so if it's public content and a public video, you can get brand exposure on your site and YouTube. If you don't want to use YouTube, we like Vimeo, and they have a beautiful embed. I have also heard others have success with Wistia, but it's is quite expensive.
Second step would be to create and upload your video to these services. Quality, size, etc. will all be determined by whatever service you like to use, but a good rule of thumb is to upload something that's at least 1080p, or 4k if possible. The embed services will do their job by helping to downsize/format video for whatever device is requesting them.
Third step would be to copy the embed code from one of these services and paste anywhere on the site that has a content editor. The preview tile/title of the video will be a part of the service that you use when you go to generate the embed code. Make sure to use the "text" version of the editor when pasting the code in. You can put this on blog posts, pages, etc. - and if you can't put it somewhere let us know and we can probably make it happen for you. If you need to loop a video, we might have to customize the embed code.