Exit west does not have a definite meaning and can be interpretated in a variety of ways, such as a simple safety exit in an emergency: a simple door that can sometimes have a lifetime.
Journey to a new place, a new country, towards new traditions, cultures and discoveries.
Another meaning it can assume is that of escape, escape of a war, from a place no longer habitable for to lack of primary resources or simply an emigration.
The sun sets to the west, so a scene exit, something that disappears.