It is a circle because, the earth is a circle, and the equator stretches all the way around the earth.
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The equator is the only parallel that is a great circle because it is centered on the Earth's axis of rotation. This means that it divides the Earth into two equal hemispheres and its circumference is the maximum possible for a circle on the Earth's surface. Other parallels are smaller circles and not great circles.
The parallels themselves are oriented in the east-west direction. They're parallel to one another, as well as to Earth's equator. What "latitude" denotes, however, is how far north or south of the equator you are. If you're located at 1° N, you're about 69 miles north of the equator. If you're at 89° N, you're about 69 miles from the North Pole. I said "about 69 miles" there because it's not exactly 69.000 miles, AND because it varies a tiny bit, due to Earth bulging out a tiny bit at the equator (because it's spinning at 1000 MPH). But don't let anyone tell you Earth is oval, because this bulge is something that we can measure. To look at it, no one would know it wasn't a perfect sphere.
Diametrically opposite lines of longitude and the equator are called great circles because they are the largest circles that can be drawn on a sphere. These circles divide the sphere into two equal halves and pass through the center of the sphere, making them great in size and significance.
The equator is also known as the line of equator, equinoctial line, and celestial equator.
All parallels of latitude, except for the Equator, are not great circles. Great circles are the largest circles that can be drawn on a sphere and pass through its center, whereas small circles do not pass through the center of the sphere.
There is only one line of latitude on the equator, and the equator is it.