Mexican Cession is the historical name which is used for the present day Southwestern United States. This area was ceded to United States by Mexico in the year 1848. This happened as a result of the treaty of Guadalupe Hidalgo that ended the Mexican American war.
The cession of the Mexican territory was a condition that was set by U.S for ending the war. Mexico risked complete annexation by the United States as the United States Troops occupied the Mexico city. So Mexico had to give in.
U.S had to pay $15,000,000 for the land. This land makes up for around 14.9 percent of the total area of the U.S territory.