Vignetting is a term that describes when the corners of an image are darker than the center. Many times this is caused by the lens that was used to shoot the image. Most lenses will exhibit some vignetting when they are wide open at maximum aperture. As the aperture is closed down, the light is more evenly distributed across the image sensor or film.
This image was shot with the Canon EF 40 f2.8 STM lens on a Canon 5DII. The 40mm STM lens has the strongest example of vignetting I have seen in a lens.
Notice how the corners are a much darker exposure than the center of the frame. This is vignetting.
Many photographers will notice significantly more vignetting on a full frame sensor compared to a crop sensor even with the same lens at the same aperture setting. This is because a crop sensor camera is only seeing the center of the image and the corners of the image are never recorded.
Vignetting is not necessarily a positive or negative quality. Many people find the effect appealing and prefer it. Some even create a vignette in post production with software like Adobe Photoshop or Lightroom. Like many aspects of photography, it is up to the creator to decide if it should be a part of the photograph or not.
Here are some other examples of strong natural vignetting from the lens
Here are some examples of images first without natural vignette, and then with vignette added in post production: