The policy of manifest destiny lead Polk and the US to enter war. Manifest destiny is the belief that it is the destiny of the US to expand their power/influence all across North America (from the Atlantic to the Pacific).
In order to accomplish this goal, the US needed some territory from Mexico. This was one of the biggest causes of the Mexican-American War (1846-1848). Fighting along the Rio Grande river lead to this war, which resulted in the US gaining a significant amount of territory from Mexico. This includes land such as California, Arizona, Utah, New Mexico, and Colorado.