Henne functions as an object pronoun, e.g.,
Han elsker henne= He loves her.
In the above sentence, "henne" is referring to the woman herself.
Hennes functions as a possessive, e.g.,
Brevet er hennes= The letter is hers.
Han leser brevet hennes= He reads her letter.
In the above two sentences, "hennes" is referring to objects that the woman owns, not the woman herself.
Hope this helps! :)