High level features are computed based on examples given to a machine-learning process. A description of this process is linked from the page that you found: https://github.com/MTG/essentia/blob/master/FAQ.md#how-it-works
This means that, in the case of tonal/atonal, we selected 144 music excerpts which a (human) listener thought sounded atonal, and 199 which they thought sounded tonal.
This means that the results therefore reflect the songs that went into the process. It could be difficult to describe the terms without giving examples. While we can't share the audio used for these models because of copyright restrictions, we are hoping to in the future add metadata to this accuracy page (song names, mbids, etc) so that people can find the audio themselves and listen to it.
To use the dataset editor, log into your account and then follow the link from your profile. Thanks for reminding me - we need to also publish a tutorial on how to do this.