This is the 665th most frequent German word.
schreiben
"Schreiben" means "to write."
Here, 'schreiben' is used to describe the act of writing, in this case, a letter.
Ich schreibe einen Brief an meine Freundin.
I am writing a letter to my friend.
In this past perfect sentence, 'schreiben' indicates the completion of the act of writing, modifying 'Geschichte'.
Er hat die Geschichte sehr spannend geschrieben.
He wrote the story very excitingly.
Here, 'schreiben' depicts the request for the action of writing, specifically a name.