The island nation the United States helped gain independence from Spain in the war was Cuba.
Cuba had been fighting Spain in its War of Independence since 1895, following earlier failed revolts. American public sympathy grew as reports described Spanish repression, while the United States also had significant economic interests on the island. After the USS Maine exploded in Havana Harbor in February 1898, the United States entered the conflict against Spain.
Congress's declaration included the Teller Amendment, which promised that the United States would not permanently annex Cuba. American forces helped defeat Spanish forces, but Cuba did not become independent immediately. The Treaty of Paris formally ended Spanish sovereignty, and the United States occupied Cuba until 1902.
A common mix-up is confusing Cuba with Puerto Rico, Guam, or the Philippines. Those territories were ceded to the United States after the war; Cuba was formally recognized as independent, although the Platt Amendment gave the United States substantial influence over Cuban affairs for years.