Before becoming the 28th US State, Texas was part of Mexico. Under Mexican control, Texas had a lot of autonomy and had 10,000 white American settlers living there in comparison to 4,000 Tejanos (Mexicans living in Texas).
In 1833, a man named Antonio López de Santa Anna came into power and he centralised the power back towards Mexico City (the nation's capital) which annoyed the Texans so they decided to rebel against Mexico.
One of the most famous battle in the Texas Revolution was the Battle of Alamo which saw Mexico reclaim the Alamo mission near San Antonio de Bexar and saw the deaths of many Texans and Tejanos following a 13 day siege.
On 21 April 1836, the Texan Army led by General Sam Houston (who the city of Houston, Texas is named after) defeated the Mexican army in an 18 minute battle. The battle cries uttered that day included "Remember the Alamo!" and "Remember Goliad!" both of which were uttered by Houston's men. After this, the Mexicans would retreat to the south of the Rio Grande, a river that forms the modern day Mexico-United States border. That same day, 21 April 1836, saw the end of the Texan Revolution.
Although Texas did get its independence in 1836, America would later annex Texas in 1845.