The description of the Spanish American War as a "splendid little war" comes from John Hay, US ambassador to Britain, when he said to Theodore Roosevelt,
It has been a splendid little war, begun with the highest motives, carried on with magnificent intelligence and spirit, favored by that fortune which loves the brave.
With those words, he explained what he meant by "splendid." The war was "little" only in the sense that it lasted only 110 days; its impact, however, was huge.
The "highest motives" that Hay referred to were the desire to intervene on the behalf of Cubans and Philippine islanders in their struggles for independence from Spain. Cubans in particular had suffered greatly in their efforts to rid themselves of Spanish rule. Over 100,000 Cubans had died from disease while imprisoned in Spanish internment camps. Americans, including Clara Barton, wanted to help their Caribbean neighbors. Additional motives for engaging Spain included the desire for strategic positions around the world and the longing to display American might to the rest of the world and assert the U.S. on the world stage. Although modern views question whether such motives were commendable, at the time most American citizens seemed ready for the US to become involved in world affairs.
Hay also thought the war had been carried on with "magnificent intelligence and spirit." Like any war, this one had its blunders of communication, so intelligence wasn't always its defining quality. Few could deny, however, the "spirit" with which it was conducted. On sea and on land, the Navy and Army respectively entered the conflict with gusto. This is best symbolized by Teddy Roosevelt, who resigned his role with the Navy to put together his one-thousand-man group of Army soldiers known as the Rough Riders. This regiment included prestigious athletes from Ivy League colleges, members of elite families, cowboys, and frontiersmen. They volunteered to help fight the war on the ground to liberate Cuba.
Hay also commented on the "fortune" that blessed the war. This refers to the relatively small number of American deaths and casualties the war claimed as well, as the momentous gains that accrued to the US upon the war's completion. Only 385 men died in battle, and the Treaty of Paris that concluded the war gave the US control of Puerto Rico, Guam, and the Phillippines, establishing the US as a colonial power.
Although to modern ears "splendid little war" sounds offensive, Hay had reasons for describing the Spanish American War with those words.