This is a perfect example of Rembrandt Lighting shot by Lee Allison on the 36exp Studio Lighting Course.
It’s called Rembrandt Lighting because it resembles the directional light used by the Dutch master. If you look up some of his paintings you will see why.
What is Rembrandt Lighting? Basically it is a fairly directional lighting set up. The main characteristic is that triangle of light on the cheek, below the eye.
Why would you want to do Rembrandt Lighting? No hard and fast reason, but it’s a reasonably atmospheric sort of light.
You have successfully achieved a good Rembrandt Lighting set up when you have a triangle of light under one eye, and you also have catch lights in both eyes, as you can (just) see in the photo above.
How do you do Rembrandt Lighting? You can do it with just one light as we have here. Just place the light to the side and above your subject and then adjust the angle until you see the famous triangle.
The triangle is caused by the shadow of the nose meeting the shadow of on the side of the face. If your light is in the wrong place, you either won’t get the triangle of light, or the shadow of the nose will not meet the unlit side of the face, and it will look wrong.
It’s just another lighting technique to be used as you see fit. You could also add a fill light, or a hair light, or a background light.