The one arm press of course develops shoulder strength and muscle. But it doesn't end there. Maybe even more than pressing a barbell, or two dumbbells at once, one-arm pressing requires serious tightening of all the muscles of your lower back and abdominals, or your "core" as the region is called now. And that is a good thing.
Pressing a heavy dumbbell or kettlebell overhead with one arm was a popular feat of strength of old-time strongmen. The great heavyweight lifter Paul Anderson could press 300 lbs. It's hard to imagine, I know, but there is video proof.
Don't overlook it as an exercise movement in an all around fitness or body building program.
I recommend exhaling as you press overhead and inhale as the weight returns. Give it a try. I think you'll realize right away its value as a upper-body compound exercise movement.