For example,
If your left hand was doing the lifting:
The right hand would be grabbing the top right of the bench, the right knee would be on the bottom right corner of the bench, your left leg would be to the straight, to the side, and you would grab the dumbbell and lift it up with your left hand.
What is this exercise called and what does it work?







Your description did not indicate how weight was lifted with the left hand. If arm is straight, then you would be using your shoulders. If the arm bends at the elbow, then biceps.
I suggest that you explore this website linked below for a similar exercise and it will provide the names of the muscles used.http://exrx.net/Lists/Directory.html
It's called 1-Arm Rowing and it works your lats and biceps