How does this feature work?

Sorry to be asking this , there is absolutely no documentation on this after googling for a while.
How does this feature work? It seems to suggest vertex static lighting is supported but when i set to vertex all i get is invalid lightmap settings

Well, your Vertex will be related to the geometry surface itself or the pixel data of vertex coloring and the texture information will be the colored pixel data which is layered on that surface when rendered and mapped via UV mapping.

The modern usage of something called Vertex Mapping is the Vertex Map restricts Polygon Areas receiving certain specific parameters or influences.

The vertex coloring is also used to influence shading for a more solid or flowing pattern with blending, such as for your geometry base color layer.

Programs such as Cinema 4D generate such things, like the video here:
https://www.youtube.com/watch?v=olft6gWL6hQ

That probably doesn’t fully explain it, but the Statistics Tool is providing the information you are setting it to display, so if you are looking at the information of static mesh lighting it will give you the data related to that.

@KnightTechDev , I understand what is vertex lighting and how UDK use that for static light ( whih can be activated by setting lightmapres to 0 )

However , I’m not aware that UE4 have them . After setting to vertex-based static lighting , I keep getting errors when building light.