Is "What a day!" a sentence? If it is, what is its subject and its predicate ?
An exclamatory sentence, or exclamation, is simply a more forceful version of a declarative sentence, marked at the end with an exclamation mark:
What an awful /What a nice day it is!
In this case it is the subject and is -the verb
Exclamatory sentences are common in speech and (sometimes) in fiction, but over the last 200 years they have almost entirely disappeared from academic writing. You will (or should) probably never use one in any sort of academic writing, except where you are quoting something else directly.