This is called vignetting, it is caused by light being blocked from reaching that part of the frame that hits other parts. It can have a number of different causes, however common causes are the geometry of the lens itself resulting in light falloff near the edges, filters attached to the lens blocking some light from reaching the corners and a lens hood partially obstructing light from reaching the corners.
It's pretty much always a trade off and since it's typically fairly well understood for a lens, there are often post production corrections that can be applied to brighten the image appropriately, at least for the well known versions of it. It might be a little harder to correct when it is the result of a filter stack.
Closing the aperture some reduces it since it blocks out the light from the edges that wasn't being blocked and thus you get less light overall, but a more even distribution of light.