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.
The War of Reform (1858–61) was a civil war (conflict among citizens of a nation) in Mexico that began three years after the collapse of the government. In 1855 revolutionary leader Ignacio Comonfort (1812–1863) became president of Mexico when he helped overthrow the dictatorship (government under the absolute control of one ruler) of President Antonio López de Santa Anna (1794–1876). Two years later Comonfort and his supporters drafted a constitution (a document specifying the laws of a nation) that removed property from the control of the Roman Catholic Church and reduced the privileges of the army. Comonfort's government faced bitter opposition to these policies, and the War of Reform broke out the following year. Giving in to political pressure, Comonfort fled the country and Benito Juárez (1806–1872), former minister of justice and minister of the interior, became president. Faced with strong opposition from supporters of the army, called conservatives, Juárez withdrew from Mexico City and set up the capital at Veracruz, on the coast of the Gulf of Mexico. At Veracruz Juárez's government had control over customs receipts (taxes collected on goods brought in by ship), which it used to purchase arms and finance operating expenses. Eventually, Juárez and his allies defeated the conservatives and reentered Mexico City in January 1861, thus ending the War of Reform. Juárez was elected president later that year. The conservatives then sought foreign aid and received it from French leader Napoleon III (1808–1873), who was interested in starting a colonial empire. The French directly challenged Juárez's authority by installing Maximilian (1832–1867) as emperor of Mexico. Juárez led the country in a successful campaign against the French, expelling them in 1867 when he resumed the presidency. He died in office, in 1872.
Further Information: DeVerona, Frank. Benito Juárez: President of Mexico. Brookfield, Conn.: Mill-brook Press, 1994; History of Mexico 4. [Online] Available http://www.emayzine.com/lectures/MEX4.html, October 25, 2000; MacMillan, Dianne M. Mexican Independence Day and Cinco de Mayo. Springfield, N.J.: Enslow Publishers, 1997; "Mexico." Electric Library. [Online] Available http://www.encyclopedia.com/articles/06747.html, October 25, 2000.