Who fought the Mexican Revolution and why?
The previous answer is not correct. The Mexican Revolution began in 1910, long after Texas had broken away from Mexico.
The Mexican Revolution was essentially a civil war between political factions within Mexico. One faction ostensibly wanted a more democratic system that would be more concerned with the welfare of all the people. This faction had become tired of the rather authoritarian rule that Mexico had experienced during the rule of Porfirio Diaz. This faction initially seemed to have won when Francisco Madero's rebellion succeeded and he became president.
But then Madero was overthrown and killed by Victoriano Huerta. Huerta was interested in trying to recreate Diaz's regime. The revolution then continued as various forces fought Huerta to try to overthrow him. These forces, now led by Venustiano Carranza, defeated Huerta in 1914. The fighting continued even so as various factions among the rebels continued to fight until 1920.
The basic idea, however, is that this was a revolution that was supposed to be for more democracy and for policies that would help the masses of people. It was fighting against autocratic rule that was mainly for the benefit of the elites.