After the 9/11 attack on the Twin Towers in New York, the US administration was quick to react to the terrorists, namely al-Qaeda. Afghanistan was the nation in which al-Qaeda had its strongest basis, as well as the majority of its leadership, so the US launched an attack on this nation. The invasion was going relatively well, and as planned, with the main goal of weakening and possibly totally destroying al-Qaeda being accomplished step by step. The end result was destruction of this terrorist organization, with its leader Osama bin Laden being captured and murdered as well.
It established the principle that everyone is subject to the law. Even the king. It also guaranteed the rights of individuals, and the right to a fair trial.
Conquered territories were often left relatively unchanged under their old rulers as long as they recognized Aztec supremacy and paid tribute. Hope this helps