"义和团运动" can be translated into English as "the Boxer Movement" or "the Boxer Rebellion".
"Boxer" refers to the participants of the movement, who were often referred to as "Boxers" by foreigners due to their practice of martial arts and boxing-like exercises as part of their preparations and rituals.
"Movement" emphasizes its nature as a social and political movement.
"Rebellion" highlights its aspect as an armed uprising or revolt against foreign influence and the Qing government's perceived collaboration with it.
Both translations are widely accepted and used, depending on the context and emphasis desired.