They give your vertex a color!
Okay, okay, there are some situations where they make more sense, like for example for weighting animation within the vertex shader, blending between textures instead of using a blendmap, using it instead of a lightmap. They are basicly just a lot cheaper than textures, don´t need you to unwrap your model, allow to tile your textures but still highlight some areas different than others in a very easy and artist friendly way and stuff like that
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-> They are great stuff, especially for things like fish or plants animations and especially on hardware not supporting vertex shader texture lookups, where you can do stuff like geometric wave animation on the cpu or somethig like that. And much more