Before the Spanish-American War, America's foreign policy was aimed mostly at expanding its own territory and protecting it fro foreign threats. The issues America had with other countries all revolved around things like that. There was the Louisiana Purchase. There was the Mexican-American War. There was the "54-40 or Fight" crisis involving England and the Oregon Territory.
Beginning with the Spanish-American War, the US turned towards expanding its power and having more of an impact on the international scene. The US then did things like taking and running the Philippines. It pushed for the "Open Door" in China. It mediated between Japan and Russia in the Russo-Japanese War and it tried to keep Japan from expanding too much in the days before WWII.
In this way, the Spanish American War represented a turning point after which the US was more aggressive and more internationally-minded than it had previously been.