You can't upload a video here like you can with pictures. However, you can copy the address of a YouTube video and use the "Insert Video" icon in the editor to "post" a YouTube video:
1. From a YouTube video, click the "Share" icon on the lower right of the video, then copy the URL address of the video.
2. Click the "Insert Video" icon on the editor (looks like a piece of film):
3. When you get the Pop up window, paste the Video URL into the field provided and click OK
Then once the video "code" is pasted into the editor, type whatever text you want (above and/or below the code), then just post your message like normal and the video should be displayed in the post.
NOTE: You used to have to remove the "s" in "https" part of the address but now that I've made the BCF completely https compliant, you no longer need to do that - just paste the video URL exactly as it is copied from YouTube.