Left without - right with Weighted Normal Modifier
Let's first explain what Weighted Normal Modifier is doing:
Face weighted normals (FWN) is a technique to improve shading for 3d
models. Shading can be improved by adding bevels and altering the
vertex normals to be perpendicular on the larger flat polygons. This
forces the shading to be blended across the smaller bevel faces,
rather than across the entire model.
To visualise this let's look at our example:
You can see here how vertex normals were calculated and gave flat surfaces and nice smooth bevels. Most important thing here is that Bevel has only 1 segment.
Where to use this technique?
Most commonly it is used for low/medium poly assets - games.
Read here about how it was used in Star Citizen: https://polycount.com/discussion/155894/decal-technique-from-star-citizen
I'm personally heavy using it for arch design. Where you can have whole building with bevels, not so good topography and still results are nice and smooth.
Using it with high poly assets sometimes also could be beneficial especially when topology is really messed up.
Weighted vertex normals improve the appearance of virtually all
geometry, and is generally superior to the traditional non-weighted
average. It works because the undesired shading artifacts are
displaced from large (highly visible) polygons to their smaller
neighbors (less visible), and thereby guarantees improved visuals in
virtually all common situations.
Check also this question with comments: Is it possible to get automatic smooth edges with flat faces without adding geometry?
You can also utilize this method by using Harden Normals in Bevel modifier - AutoSmooth need to be turned on also.