It is a revolutionary movement led by Fidel Castro that overthrew the regime of Fulgencio Batista in Cuba (1959). Its name commemorated an attack on the Santiago army barracks on July 26, 1953. The movement began formally in 1955 when Castro went to Mexico to form a disciplined guerrilla force. The leaders of the movement remaining in Cuba to carry out sabotage.
Source: Encyclopedia Britanica

The flag of the 26th of July Movement is on the shoulder of the Cuban military uniform. The 26th of July Movement was the revolutionary organization led by Fidel Castro that in 1959 overthrew the Fulgencio Batista regime in Cuba. Its name originated from the failed attack on the Moncada Barracks, an army facility in the city of Santiago de Cuba, on July 26, 1953.