The Spanish cession refers to either the "Florida Purchase" or "Adams-Onis Treaty" that was acquired in 1819 or to the Mexican Cession of 1848 where the United States acquired land in what is now modern-day Arizona, California, New Mexico, Nevada, Wyoming, Utah and Colorado. The U.S. inherited West Florida, East Florida and areas that were south of the areas acquired in the Louisiana Purchase.
The reason for the Florida cessation was that U.S. President James Madison laid claim to the area at a time when Spain's rule in the area had been weakened due to the French invasion of Spain led by Napoleon. The reason for the Mexican cessation was due to the fighting over the U.S. and Mexican borders as well as the Mexican-American war.
When Texas became a part of the U.S., Spain was upset and a border disagreement ensued. Texas had 389,000 square miles of territory that had belonged to Spain and, therefore, Spain was upset that it was now a part of the U.S. This time period, the 1800s, was a busy time period for the U.S. when it came to newly acquired properties, including the Alaska Purchase, the Gadsden Purchase, the Red River Valley acquisition and the Louisiana Purchase.