This new feature basically lets you watch a shared video while it is being downloaded to your phone. This makes it easier for the user to watch the video without having to wait for the entire video to download.
Currently the feature is only available on beta version of WhatsApp v2.16.365. If you like give a try to test this feature then, you can download the apk file for the video streaming feature.
As the feature is already available in beta version of the Android app, hence we can expect the feature soon for everyone.