The look Rue's sister gave Katniss on her victory tour told Katniss that she needed to say something to the people of District 11 about her sister, Rue, who died when Marvel threw a spear into her stomach. Before Rue died she was of great assistance to Katniss and a great friend to her, as she reminded Katniss of her sister, Prim. When Rue died Katniss covered her fatal wound with flowers she picked, and gave the people of District 11 the farewell gesture that they use back in District 12.
Rue's sister made it clear to Katniss that if her sister and her district partner, Thresh, went unthanked then they would not be forgiven. So Katniss gave a long and heartbreaking speech to the people of District 11 about how she didn't know Thresh but, he saved her from Clove and also spared her life, and how much Rue meant to her and that she won't be forgotten. That speech is what inspired District 11 to start an uprising.