wrapping circular black frame for video - What is this effect called?
it's a vignette.
Here's a tutorial on how to do it.

If you add a black solid layer to a comp, then feather the edges, and invert the mask, you'll get the basic effect.  Beyond that, some people used coloured solids (e.g. just off-black in one colour or another).  You can also apply a blur or defocus effect towards the edges of the image, if that's the look you're going for.