This opening line means roughly, “Mexicans, at the cry of war.” It is a call addressed directly to the Mexican people, using a dramatic nineteenth-century patriotic style. The line imagines the nation hearing an alarm or battle cry and responding together.
For an English speaker, the important words are grito, meaning “shout” or “cry,” and guerra, meaning “war.” The phrase al grito de guerra does not mean someone is casually yelling about war; it means “when the war cry is heard” or “at the call to battle.” The anthem begins with readiness and collective defense, not with a quiet description of the country.