Grassroots democracy is a tendency towards designing political processes where as much decision-making authority as practical is shifted to the organization's lowest geographic level of organization. This is called the principle of subsidiarity.
To cite a specific hypothetical example, a national grassroots organization would place as much decision-making power as possible in the hands of a local chapter instead of the head office. The principle is that for democratic power to be best exercised it must be vested in a local community instead of isolated, atomized individuals, essentially making it the opposite of national supremacy. As such, grassroots organizations exist in contrast to so-called participatory systems, which tend to allow individuals equal access to decision-making irrespective of their standing in a local community, or which particular community they reside in. As well, grassroots systems also differ from representative systems that allow local communities or national memberships to elect representatives who then go on to make decisions.
The difference between the three systems comes down to where they rest on two different axes: the rootedness in a community (grassroots versus national or international); and the ability of all individuals to participate in the shared decision-making process (participatory versus representative.)