Verify will appears, for example, after the creation of a communication. It is here to remind you to verify the information registered. When you do a verify action, a note in the action history is registered and you can see who verified the information.
It is also useful when you use the field 'Needs verification" in Analytics. When a communication is edited, it is then classified as 'Need verification', so the new information can be verified.
It is the same purpose for grievances and issues.