Ancient Greek cosmology (at least, the version you are probably thinking of) saw the universe as a sphere and viewed matter as being made up of five elements: earth, water, air, fire, and quintessence.
In this model, the earth occupies the center of the universe and is fixed in place. The elements were ideally arranged around the center of the universe in concentric shells....earth, then water, then air, then fire, then quintessence. Objects containing an element would seek to find the "level" of that element: put a stone in water, and it will wind up below the water, while an air bubble would rise above it. Flame and heat rise in air. Water falls. Etc. Quintessence was only found in the heavens.
Since all of this happens relative to the center of the universe/earth, it would work identically no matter where on the surface of the earth you were. A key difference between this worldview and more modern views on gravity is that there's no connection between the forces that, eg, cause an apple to fall and those that dictate the movement of the planets.
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