Inserting video into a web page is not a trivial operation. basically, until HTML5 support is more widespread (read universal) there is no video tag. So you need to insert code to load a flash video player. This necessitates that your site have a video player available to it - and unless you've added one, you do not.
Additionally, the html code to embed the flash varies between different browsers. Probably the most common method nowadays is to insert the video player, and specify the media (file) for it to play via javascript. Again this necessitates having the javascript in place and having a div or similar container with a specified 'id' for the javascript to substitute the video into dynamically.
Like I said - this is non-trivial, ie not straightforward.
Withn Joomla the most frequent method of inserting video is via a plugin whereby you embed a 'tag' marked with curly braces which the php substitutes for working html,javascript,flash at runtime. The JCE editor has a button for this - I think it may be an extension. Alternatively AllVideos, and AllVideos reloaded are well established plugins that allow insertion of videos from local website or from remote sites (Amazon S3 servers, YouTube, Vimeo, etc).
The standard Media Manager, and the file manager screens (such as when you click to insert images) should allow uploading of videos, but you may have to add the correct mime types within the global configuration screens.
I'm sure the Joomla Extensions Directory (JED) should have many other methods available too: http://extensions.joomla.org/