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It is pretty self-explanatory. It verifies does your model meet some quality standards. It helped me identify that one of my models was not manifold (Even though it was when I first exported it... there is some bug with Blender when exporting files).
One thing I don't like about it is how it grades all models the same. For example, all my models are made for 3d printing therefore textures and UV-s should not be included in the verification score of 3d-printable models but they do in their current form.
Was this feature added recently? I can't remember not seeing it on my dashboard. Either way, none of my models have been reviewed yet, they must be swamped with verification requests.