From Universe Today,
The Latin name for our galaxy is Via Lactea. It translates literally as Road of Milk and is so called because of the pale band of light formed by stars in the galactic plane as seen from Earth. It appears to be a milky patch of sky that rings the Earth. The name of the person who came up with this reference has been lost to prehistory, but it was in such common use by the time Galileo realized it was an area packed with stars, that any other name could not have been used. It was hundreds of years after Galileo that it was realized we were looking at an edge on view of our own galaxy, one of billions in the universe.