Simply put, it's a .308 necked down to .284. Better ballistics, less recoil, less powder are benefits over it's parent cartridge. Ideally suited for deer sized game and shines in a lightweight bolt rifle.
Here's a good article about the Model Seven/7-08...
Howard Brant, 1989
I re-barreled my .308 Model Seven to 7-08 over the winter...
120gr TSX @ 3000 fps out of a 7lb bolt gun with very mild recoil. Bump it up to 140gr TSX and go elk hunting.
What's not to like?