The Spanish American War marked the first time since the War of 1812 that the United States involved itself in a war involving a foreign nation. It also marked the beginning of the end for America's policy of self imposed isolation, and the beginning of American territorial possessions outside its continental limits.
The United States for many years had not involved itself in affairs of other nations outside the Americas. This was pursuant not only to the Monroe Doctrine but also to George Washington's admonition that the U.S. should remain "free of entangling alliances." The Spanish American War was largely precipitated by rival New York newspapers competing for subscriptions and who published lurid (and sometimes untrue) accounts of Spanish atrocities in Cuba. The war broke out after the sinking of the U.S.S. Main because of demands made by the U.S. to which it knew the Spanish would not agree. As a result of this very short war (Secretary of State John Hay called it a "splendid little war.") The U.S. gained possession not only of Puerto Rico but also Guam and the Philippines. Although the Philippines were eventually liberated, Guam and Puerto Rico remain U.S. possessions.
Second, it showed American dominance within the shere of the Americas, and extending even way out into the Pacific.
Third, it effectively created an American Empire, and the Pacific portion of that empire would put the US in the way of expansionist Empirial Japan, some 40 years later.
Taken all together, the above points all fit together to announce the arrival of America as a major power, in the same class (although perhaps not quite on the same parr) with France and Britain. Spain was obviously no longer a contender for empire, and eclipsing that one European Impirial nation was a major step forward into the first ranks of power for the US. The victory over the Spanish Fleet in Manila Harbor also strengthened the US military view that a strong Navy was the most critical element of America defense policy. That point of view is still deeply influencing our defense outlook today.