The description of Helen's fit at the table is excellent because it shows what Annie Sullivan is up against. It also demonstrates that Annie is at least as stubborn and strong-willed as Helen, indicating that Annie will win out in the end. It shows Annie's commitment to Helen because she knows she can't teach Helen language unless she can control her behavior.
At the table, Helen behaves in her usual fashion. She runs around the table, putting her hands in other people's food. She refuses to sit in her chair, eat from her own plate, use a spoon, or fold her napkin. It has been the family's practice to ignore her, but it's really impossible to do. The scene is comical in its description of what happens once Annie asks the family to leave. Annie must repeat again and again and again the behaviors she wants Helen to learn. In the end, Annie is successful, but she looks like she's been in the fight of her life. This scene is a war of strong wills.