VideoPress is a feature of Jetpack and makes showing videos on WordPress way better. Here’s three biggies for me:

1. Performance. Videos are optimzied and cloud-hosted (rather than coming from your own server) and served with fancy video hosting techniques like adaptive bitrate streaming.
2. Custom. The player has many more fancy features than the default HTML player has, and can be customized.
3. Mobile. Don’t bother with a poster attribute (unless you want to), you’ll get a video player than looks like a video player on mobile, rather than the default blank nothing of HTML video without a poster graphic.