It is only possible to embed a Dropbox video if you have a Dropbox Pro account.
IMPORTANT: As of September 2017, Dropbox will no longer allow this.
After that time you will no longer be able to embed videos or other content that is hosted on Dropbox.
If you would still like to know how to do this, add a video element to your page and select the "Custom Embed" option.
The video will need to be in your Public Dropbox folder.
Get the link for the video and add it to the code snippet below:
<iframe width="100%" src="YOUR_DROPBOX_URL_HERE?raw=1&autoplay=1" frameborder="0" allowfullscreen></iframe>
Only replace where it says YOUR_DROPBOX_URL_HERE
Because Dropbox will no longer allow this after September 2017, it is highly recommended that you use a service such as YouTube, Vimeo, Wistia, or Amazon S3 to host your videos.