to introduce someone to an unfamiliar thing; to become familiar with something; to get to know something; to tell someone the facts [about someone or something]. (See also acquainted with someone; acquainted with something.) It took a month for the new attorney to acquaint herself with the facts in the case.
To make someone familiar with something or someone: The next chapter of the textbook acquaints the student with several new concepts. I am not acquainted with the mayor of this town.