Bethany = "house of dates" or, "house of misery"
1] a village at the Mount of Olives, about two miles (3 km) from Jerusalem, on or near the normal road to Jericho (see map)
2] a town or village on the east bank of the Jordan, where John was baptizing
derivation: of Aramaic origin
http://bible.crosswalk.com/Lexicons/Greek/grk.cgi?number=963&version=kjv

Additional information:
"All things considered, the most probable opinion is that there was a Bethany fifteen furlongs from Jerusalem, and another across the Jordan. The name of this latter may have been a transliteration of a Hebrew phrase meaning "the place of the ship". Bethany across the Jordan has shared the fate of many other Biblical sites which have disappeared from the earth."
Quoted from: http://www.newadvent.org/cathen/02532a.htm

Comment:
The point of reference in the quotation (shown above in "Additional Information") is Jerusalem. When the author of that quotation used the phrase "across the Jordan", the author therefore meant "across the Jordan [as viewed from Jerusalem]". The Jordan river is east of Jerusalem (see map). The author's phrase, "across the Jordan [as viewed from Jerusalem]", therefore means "east of the Jordan river". This meaning is the opposite of what is meant by the phrase "beyond Jordan" in paragraph 003-d, paragraph 046-d, and paragraph 081-a. The phrase "beyond Jordan" means "west of Jordan" because the first time the Children of Israel saw any of the land "beyond Jordan", they  saw it while looking west across the Jordan river. One possible conclusion is that there never was any village named "Bethany" east of the Jordan river. If that's true, then the assertion, that John the Baptist was baptizing at or near a town named "Bethany" which was located east of the Jordan river, is not correct. The location on the Jordan river at which John the Baptist was baptizing therefore seems uncertain, contrary to the assertion by CrossWalk.

A link to each occurrence of this word in the homepage:
1] Bethany
2] Bethany