Currently, this experimental feature is available for premium subscribers which is not surprising as subscribers already have the facility to download mobile videos.
In the web version, this download button will be available with the share option when opening a video, while it will be discovered in the three dot menu while browsing.
When a video is downloaded, it will be saved in the offline YouTube video. It will be possible to watch these videos in 144p to 1080p resolution.
Apparently any video can be downloaded with this feature which will depend on the available storage.
It is not possible to say whether this feature will be available to all users or when it will be officially introduced.