Due to the nature of the email format, you can't embed videos into emails. Instead, there's a couple of alternatives:
1. Link to the video
If the video is hosted somewhere (e.g. YouTube or Vimeo) you can just link to it. A popular option is to upload an thumbnail image of the video and link the image to the video.
2. Use a GIF
You can embed GIFs in emails and they will play. We recommend Cloudapp as a tool for easily making GIFs.
Once you have a GIF, you can add it to your email using the image upload button (note that GIFs will take longer to process than a typical image).
Here's a quick demonstration (and yes, it's a GIF within a GIF - because we love GIFs so much):