It's mostly, when you just make your site with amazing, helpful, etc. content and you take care so well, that the result is (later) as you used a lot of SEO (but you didn't). The Green hat SEO is something like hatless SEO, when you make the website for the people and the visitors, not for the 'machines' (search engines, bots, crawlers and so on).
I think some good simple example maybe a viral website (a very popular website), which owner has no idea of SEO (or didn't use some particular SEO means), but the users liked the website and started to visit it often, to share it, to popularize it offline (to brand it in one of another way) and then all these measures are as a result of the 'hatless
', i.e. the green SEO
(he, she or they just did the viral website and 'it' took care by itself
All I can recommend is green SEO + (at least some) white SEO