bit of a late reply, but verified users are users who have a checkmark next to their username. as far as i can tell, it doesn’t grant you any benefits other than bragging rights (which is kind of annoying so don’t do that). there’s no official process for getting verified, and asking jeffalo or any other moderators if you can be verified will only hurt one’s chances of getting verified.

To prove someone is who they are. For example, if there was a person named “griffpatch” it’s probably a parody account, but if they are verified, it means that the user proved to the mods that they are actually “griffpatch”.