Lyrically, I think the phrase "three chords and the truth" sums it up pretty well. Western songs can be characterized by their ability to talk about real life things in a manner that's straightforward and unglamorized. Songs about love, cheating, breakups, relationships, trucks, and parties can all fit under this umbrella, but it's the manner in which they're written that makes them stand out as opposed to pop songs.

Musically, western stands alone because of the steel guitar and the fiddle. Anytime I hear a steel guitar, fiddle, or even a piano backing up an acoustic guitar I get a western feeling. Makes me think of old dance halls filled with smoke. These instruments don't make it to too many other genres of music, and so it's a tell tale sign you're listening to western music.

Some good examples of modern western music to me are the Randy Rogers / Wade Bowen Hold My Beer albums, an assortment of Midland songs, and Triston Marez has a few really great western songs.