In order:
-Home\
-My kin\
-Blue skies\
-The Swampers\
Jokes aside, the main thing in the song is that Alabama is home. Sticky sweet watermelon juice dripping down your chin in the humid summer heat, the blues of the Shoals area, the kudzu creeping along the roadside - these things may mean nothing to you, but they scream home to someone from Alabama.
It's worth noting that the song is a little bit tongue in cheek, according to Ronnie Van Zant. They put in audible boos for desegregation opponent Gov. George Wallace. Though the cowriter Ed King also contradicted that interpretation in 2009.
That said, it seems to be a bit of an ironic song.
But for actual important things from Alabama, Marshall Space Flight Center is a major NASA research center in Huntsville. MSFC lead design and assembly for the International Space Station. I believe Huntsville is currently the fastest growing city in the US, and it's a major city for hospital workers and automotive manufacturing as well.
The Muscle Shoals area has always been known for its music, as well, whether originating from or just recorded there. If you consider that important, which I do. Just look into anything recorded in that area. You'll be surprised.