1:14 in this video
This is great for developing the stabilizing muscles of the shoulder joint or when you're in a gym without any heavy weights (such as a Planet Fitness).
The Single-Arm Bench press really forces you to focus on your form, specifically driving your legs into the floor and engaging your core.
Tension creates stability, so if you're whole body is not tense, then there's a good probability you're going to fall off the bench and embarrass yourself.
I also use this exercise a lot with our athletes that are throwers or coming back from an upper body injury.
This allows them to focus on one arm at a time, which is much easier than worrying about keeping two in the right position.