An exclamatory sentence, or exclamation, is simply a more forceful version of a declarative sentence, marked at the end with an exclamation mark:

The butler did it!

How beautiful this river is!

Some towns in Upper Canada lost up to a third of their population during the cholera epidemics of the early nineteenth century!

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. Note that an exclamation mark can also appear at the end of an imperative sentence.