The board supports videos from YouTube. To embed your video, surrounding the URL with [youtube] tags as shown below:
This will be displayed as:
PS: It does not matter whether you specify http or https above, it will be mapped to https before display.

Vimeo is supported too, but be certain the embedded option is allowed:

Vimeo FAQ wrote:Users have the power to disable embedding in their privacy settings. If you aren't seeing the embed option, it means the owner of the video has disabled it. You cannot disable embedding without making your video private.

Note that Vimeo supports HD quality video, but it's a "premium" subscription feature. Be aware that if you use Vimeo premium features and let your subscription lapse, future HB visitors will not be able to see your video and may not be able to understand the context of your contributions to HB.

Below is an example of the markup:
And the result: