"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 called "Boxers" by foreigners due to their martial arts practices.
"Movement" emphasizes its social and political nature as a significant upheaval.
"Rebellion" highlights its aspect as an armed uprising against foreign influence and the Qing government's perceived collaboration with it.
Both translations are widely accepted, with "the Boxer Rebellion" being more commonly used in historical contexts.