The idiom, …have come a long way, is based on one of the most common metaphors in English: Life is a Journey. In this case, the distance traveled symbolizes change in a person’s life or character—or in the development of a project or practice, such as a business or art. So, to come a long a way means “to make a lot of progress”. Here are a few sentence examples:
From poverty to wealth and fame, she’s come a long way.
Pat used to be a terrible musician, but he’s come a long way now.
You have come a long way since your immature college days.
This phrase has a companion idiom, to have a long way to go, which means “to have much room for improvement,” i.e., to have some faults which should be fixed.