The Texas Panhandle is the region of the state of Texas which includes the northernmost 26 counties in the state. It is a rectangular area bordered by the state of New Mexico to the west and the state of Oklahoma to the north and east. The southern border of Swisher county is considered to be the southern boundary of the region.  http://www.tsha.utexas.edu/handbook/online/articles/view/PP/ryp1.html
Most of the western half west of the Caprock escarpment and north and south of the Canadian River breaks is rather flat terrain. The largest city in the Panhandle is Amarillo, Texas. The relatively flat land gives way to Palo Duro Canyon southeast of the city, the second largest canyon in the United States.