To "Bounce" an attack you send a single troop to SUPPORT the target you are attacking. Using an AH is best because of their speed. You can send AH long after the initial attack was launched.
Your troops will never attack a castle that is supported by you. When your attackers find your troop supporting, they will turn around and go home without a fight.
This can be used to spare a defender a humiliating defeat, spare yourself massive troop loss, prevent serious problems if you mistimed attacks, or prevent a war if you attacked an ally or other non-sanctioned target.
Most of all, this trick can be used to save silver. You will lose all silver sent on an attack in any other case, even if you recall manually before the first battle round. If you recall a silver attack, your troops return but silver is spent.
If you Bounce an attack with supporting troops, your silver and troops return. Sometimes, they even return home instantly without the long march back.