Fidelity is how accurately the monitor can reproduce the image. This encompasses the color spectrum that the monitor can output, the contrast, brightness, etc.
A high fidelity monitor will look extremely accurate to the way that the image should look. A monitor that's less accurate may show the image as slightly blue, maybe a bit darker or with higher contrast, maybe it can't display some edges of the spectrum or can't display true black.
It's not that important for gaming though, it's usually important for art work.