Rebound is an ability that appears on some instants and sorceries from Rise of the Eldrazi. Rebound is technically a static ability that generates a replacement effect when the card is a spell on the stack. As long as the Rebound spell was cast from your hand this replacement effect exiles the card instead of putting it in your graveyard when it resolves and generates a delayed triggered ability . This potential delayed triggered ability will trigger at the beginning of it controller’s next upkeep. When this triggered ability resolves this player may play the Rebound spell again without paying it’s mana cost.
It is important to note that the Rebound ability will not do anything if the spell was not played from your hand. This is what prevents the Rebound spell from being cast over and over again. Also, the spell will not Rebound if it is countered in some way; either by a spell or ability or by becoming countered on resolution. In both of these instances the card will go to the graveyard and not be exiled.
When the delayed triggered ability resolves in your next upkeep you may cast this card again. It is a new spell, so it can have targets and choices that are different from when it was initially cast. Additionally, you do not have to cast it again if you do not want to. (If the controller of the Rebound spell forgets to cast it it is assumed that he chose to not cast it the second time.)
When the Rebound spell resolves after being played the second time it will resolve as normal and go to the graveyard. However it if it is not played when the delayed triggered ability resolves it will remain in the exiled zone.
In a tournament setting you are not allowed to put the Rebound card on your deck to remind you of it’s delayed trigger, however you can put a different small marker on your library as a reminder.