From Envirowiki

Grassroots is a descriptor for a kind of organising that is "bottom up" -- that is, driven by people working together in communities, rather than imposed by people with power or weapons.

The term is generically applied to environment groups that are community-based (and often under-funded) and is used in opposition to high profile and wealthy NGOs. Properly though, a grassroots group would be working to bring about change among the grassroots -- the people -- rather than making use of lobbying (for example) to bring about change.