Having a responsive website is a must. But having mobile-friendly video is just as important.
1) Use YouTube or Vimeo- do not use your own server or player. It will take too long to load. Let YouTube handle the bandwidth. Their players conform automatically to viewers phones.
These sites will also convert your video to mobile friendly formats.
2) Keep It Short- :60 or less. The golden minute is key. Viewers would rather watch five (1) minute videos than a 5 minute video.
3) First Five Seconds- You have this much time to get viewers attention. So make sure your message is on key.
4) Have a Call To Action- When people view videos on mobile devices, it takes up their whole screen automatically. Give them a reason to respond.