Most people are used to going to an office, and having a commute. A lot of our decisions are being influenced because of it: Where we move to, how we life, whether we own a car or not.
Being location independent means, that someone is not bound to a specific location – for example through a commute. In general, most remote workers are at least to some degree location independent. They may sometimes not work from anywhere in the world (because of timezones), but almost all of them are free to choose whether they live in the city, the suburbs, or a cabin the woods in the middle of nowhere.
Other than being very convenient, it's giving us a preview of an upcoming sociological shift: If you can work from anywhere, who lives in the city, and who prefers to go back to a village or smaller community?