Warrant cards

The answer (as an owner of such a document) is this. A warrant is an authority (normally on behalf of the state' legal machinery, however the queen may also issue some) to conduct a particular activity. Examples include Arrest Warrant to stop and detain someone and Search Warrant to give authority to enter property. In the case of the original question, the police warrant give the named person authority to do certain things beyond those of the normal citizen such as stopping someone merely on suspicion of having committed a crime.