This policy must take root at the grassroots level to be effective.
Tips
culture
There is also a real plant called 落地生根 (Bryophyllum pinnatum, 'air plant') whose fallen leaves sprout new plants wherever they land — the literal image behind the idiom.
usage
Two main senses: (1) a person settling permanently in a new place, (2) an abstraction (policy, idea, technology) being adopted deeply at the local level. Context tells you which.