A banner is a long strip of cloth with something written on it. Banners are usually attached to two poles and carried during a protest or rally.
e.g. ...a large crowd of students carrying banners denouncing the government...
e.g. A big banner was draped across one of the streets saying, 'Idaho Falls Says NO to Drugs.'
If someone does something under the banner of a particular cause, idea, or belief, they do it saying that they support that cause, idea, or belief.
e.g. All countries march as one nation under the banner of friendship.
e.g. Under the banner of education, we herd our children from ballet to basketball and back again.