"Horen" is the verb "to hear." Literally translated it yeilds: "on again hearing" The phrase is equivalent in meaning to "until the next time I hear from you" or, more simply, "goodbye."
This phrase is properly used at the end of telephone conversations.
Related to Auf Wiedersehen and Auf Wiederlesen.
would like to point out that the o should have an umlaut
. Auf Wiederhören