There are two ways of including a video in your website. You could upload the video to your web server — a process you'd have to complete manually and not through the Media Manager because the file is almost certainly too large. Playing videos hosted on your web server may cost you a lot of money in bandwidth costs. Bandwidth, in this context, is the amount of data transmitted from your site. Your web host gives you an allowance for bandwidth each month. If you exceed it, you will pay lots of money. With video, it's very easy to exceed that bandwidth limit quickly.
Alternatively, and definitely the preferred method, you can post your video on YouTube. They will take care of the bandwidth costs, and you don't have to fiddle with uploading the video to your web server.
Once you have posted a video on YouTube, you might want to show the video on your Joomla website. Or perhaps you've found a video elsewhere that you'd like to include. Either way, the steps are the same once the video is posted on YouTube. What you will do is embed the video on your web page. Embedding means the video itself lives on YouTube, but you can see the video played on your web page. Bandwidth costs are still covered by YouTube, not by your web host, so this is really the best solution for most people posting videos on their websites.
There's plenty of help available ...