Anything western comes from the west, like a western wind that blows your hair sideways. Western also refers to anything from that half of the world — North America and Europe — as well as old cowboy movies.
Although western literally refers to anything in the west, like that wind or a direction on a compass, the Western world refers to the culture of the USA and Europe. The other is Eastern society, which includes Asia. They aren’t as popular now, but kids used to watch Westerns, also known as cowboy movies. If you go to a store that sells Western wear, you might walk out with a ten-gallon hat and red cowboy boots. Yeehaw!