An equator was an imaginary line that was equidistant from the poles and perpendicular to a planet or star's axis of rotation. This line divided the astronomical body into two hemispheres, the northern and the southern.
The debris cloud following the impact of an asteroid on the surface of Terra Nova reached to about ten or twelve degrees north of the equator. (ENT: "Terra Nova")
892-IV had a diameter of 7917 at its equator. (TOS: "Bread and Circuses")
Norcadia Prime featured an equatorial subcontinent. (VOY: "Tsunkatse")
On July 2nd 1937, trying to fly around Earth, Amelia Earhart and her navigator, Fred Noonan, took off from New Guinea abord an airplane, and they were headed east around the equator, but they vanished somewhere in the South Seas. (VOY: "The 37's")
In 2375, the star Monac had a magnetic instability near its equator, which allowed the IKS Rotarran to trigger a solar flare. (DS9: "Shadows and Symbols")