Why did James K. Polk want to annex Texas

He was a strong believer in Manifest Destiny

Polk ran on an a pro-Annexation of Texas platform in 1844 for a few reasons. One was that there were already Americans living in that territory illegally, and he wanted to protect them. Another is that he wanted increased buffer between the more settled areas of the United States and Mexico. The biggest reason though, was the notion of Manifest Destiny, or the idea that the US was destined to expand across the entirety of the continent, and the annexation of Texas was just the next logical step in that process.