Here, "ramparts" refer to the walls or embankments surrounding a fortress or other defensive structure. During the War of 1812, the United States fought several battles against the British, including the Battle of Fort McHenry in September 1814. During this battle, the American flag flew above Fort McHenry throughout the night, even as British ships bombarded the fort.
The sight of the flag still flying after a night of heavy fighting inspired Francis Scott Key, an American lawyer, to write the poem "Defence of Fort M'Henry," which later became the lyrics of "The Star-Spangled Banner." In the poem, Key described seeing the flag waving triumphantly over the ramparts of Fort McHenry, a symbol of American resilience and victory.