I assume that you are talking about the War of the Reform in Mexico.  This was a war that was fought between what are known as Conservative and Liberal factions within Mexico in the late 1850s and early 1860s.

The Conservative and Liberal factions in Mexico had been fighting just about ever since the country became independent and they would fight pretty much up until Porfirio Diaz became dictator in 1876.

This war started when the Liberals took power and introduced the Constitution of 1857.  This did things like taking power away from the Army and the Catholic Church.

The best known figure from this war is Benito Juarez, who came to be the head of the Liberal faction.