From Ohio History Central
Architect John Eisenmann designed the Ohio state flag in 1901. Ohio was participating in the Pan-American Exposition in Buffalo, New York, and desired a flag to fly over the Ohio Building at the fair. The state legislature officially adopted the flag on May 9, 1902. The shape of the flag is known as a burgee.
Eisenmann described the flag's symbolism thusly:
The triangles formed by the main lines of the flag represent the hills and valleys as typified in the State Seal, and the stripes the roads and waterways. The stars, indicating the thirteen original states of the Union, are grouped about the circle which represents the Northwest Territory; and that Ohio was the seventeenth state admitted into the Union is shown by adding four more stars. The white circle with its red center, not only represents the initial letter of Ohio, but is suggestive of its being the Buckeye State.