West is a destination, or a point on the compass, western is where one is from (or anything really) I am from western Kentucky. To the west of here is a statue. How far west do I have to go? You would never use western in direction giving. However western is also a type of country music. So be aware that the difference is minor, but important.
The answers above are certainly correct. However, also consider these contexts:
“He is a westerner, he can’t eat with chopsticks” This person is from the western half of the world.
“North Korea is always concerned about the west.” Again this is a reference to the western part of the world, also called the Western hemisphere.
“Drive Throughs are a very western idea, in the east we like to enjoy our food.” In this sentence the person is talking about the cultural differences between the east and west. Again, these are references to the eastern and Western hemisphere.
China is an “eastern country”. The United States is a “western country”.
Sometimes when people talk about east and west they are simply giving directions to a location as explained by the others.
Other times these are references to cultural and political differences between the Eastern and Western hemispheres.