A ginger group is a formal or informal group within, for example, a political party seeking to inspire the rest with its own enthusiasm and activity.
A ginger group actively works for more radical change to the policies, practices or office-holders of the organisation, while still supporting the general goals of the organisation.
Like "to ginger up," the term comes from the use of ginger root to make a horse seem more lively, or to add flavour or spice to food and beverages.