The word 'wordiness' is a noun, a word for the use of too many words in a sentence that makes it difficult to recognize the essential thought that it is trying to convey.
A noun functions as the subject of a sentence or a clause, and as the object of a verb or a preposition.
Examples:
The wordiness of your sentences detracts from the message of your essay. (subject of the sentence)
I'm trying to discern the information that the wordiness obscures. (subject of the relative clause)
Your essay uses wordiness to disguise your lack of real information. (direct object of the verb 'uses')
My essay got a low grade for wordiness. (object of the preposition 'for')