Do you remember short adjectives and participles? They are used in Russian as predicates only.

Какой/такой are pronouns corresponding to the full form adjectives/participles while каков/таков correspond to the short form ones.

The effect of каков/таков used instead какой/такой is an emphasis. You can translate it, for example, by the word "exactly".

Какова Ваша репутация? - What exactly is your reputation?
Таково мнение... - That's exactly the opinion...