What is the importance of the phrase 'from the halls of Montezuma'?

A line from the US Marines' anthem, it refers to the US victories in the Mexican War. "Montezuma" is a close approximation of the name of the Aztec king whose people were subjugated by the Spanish Conquistadores. At the time it was written Mexico City and "the shore of Tripoli" in present-day Libya were the furthest reaches of American military influence.