It’s called “Reclined Twist”. You relax in the pose while holding your bent leg towards the opposite side. The video above shows a variation of the pose, where your knee is upright; in the traditional pose, your knees are stacked over each other and against the floor, as this (much longer) video demonstrates.
You can lie in it for 10 deep breaths on each side or for 10 minutes.
As Bottom Line Publications points out:
This simple twist releases tension in the spine, hips and back, which can interfere with a good night’s sleep. The deep breathing helps you wind down, allowing you to release worries.
I find it also helps with achiness in the shoulders and neck (especially if you turn your head to the opposite side of the bent knee), and Yoga Journal says it can help cure a sluggish digestion (by wringing out your insides, I guess) and low energy. Don’t worry, it’s not too energising.