The intro video on the homepage shows the actual software in action at around 53 seconds (mouse over the video to unveil the seek bar).
The best video you can show for this is your JIRA board where everyone can update it in realtime in a team meeting with remote teams.
Don't bother with the animations, they make your product look not real! Very impressive.
A lot of browsers disable audio on auto play videos. The fact that the controls are also hidden and the background color being the same as the website, it just looks like an animation, not a video. So some icons move but the meat of the video doesn’t start until after people will have disengaged.