It is from the Greek, meaning "milky circle". The galaxy is a flattened disk, and we are inside it. So from our viewpoint it looks like a circle around the sky. They didn't have telescopes, so all they could see is a faint white band.

This is an all-sky view with our galaxy oriented horizontally. Sagittarius is a dwarf galaxy mostly hidden by the center of ours. It is on the other side. It is the nearest galaxy to our own, at 50,000 light years, and orbits the Milky Way. The two blobs on the lower right are the Magellanic Clouds, the next nearest, and also orbit the Milky Way. They are about 3 times farther, and much larger than the Sagittarius dwarf. Both will end up merged with the Milky Way eventually.