An exclamatory sentence is a sentence that ends with an exclamation mark, also known as an exclamation point.  It expresses strong emotions, such as excitement, surprise, joy, emphasis, shock …

“Cut out all these exclamation points. An exclamation point is like laughing at your own joke.”   F. Scott Fitzgerald

Yes, we tend to use exclamation marks and exclamatory sentences a bit too frequently in emails and texts and other informal writing but using the exclamatory sentence is not advisable for formal or business writing.

examples of an exclamatory sentence

Ow! That hurt!
Don’t leave me!

You use an exclamatory sentence in direct speech when you shout or speak loudly:
‘Don’t run!’ she screamed.

Exclamation mark usage dates back to the 15th century.  In a famous Seinfeld episode, the Elaine character had a fight with her boyfriend that ultimately led to a breakup when he did not use an exclamation mark in a message he left her about her friend having a baby
We like to use more than one exclamation mark if we want to really make a point!!!
Used after interjections, such as commands and exclamations,  an exclamation mark, also known in the olden days as  a “note of admiration”, is used to express excitement, as in “I am so excited!”
The exclamatory sentence enables you to express yourself in an exaggerated way.  Do not use the exclamatory sentence too often, however –  your statements will begin to sound insincere.