For Earthlings, the Galaxy refers to the stellar system in which the solar system is situated - one of the vast galaxies in the universe.
But for the aliens, the Galaxy had a special meaning. This may be difficult to understand, but take this as an example:
In ancient China, there was a degenerate young man with an education level between the 2nd year of high school and the 2nd year of college. On a certain day on his way back from the brothel, he passed by a river and found a carp dying in a mud ditch.
The fish should be thankful that the brothel that the degenerate frequented provided food, so the degenerate was stuffed to the throat and had no interest in turning the fish into food. He even performed a rare good deed - he threw the fish into the river.