An appeal bond is a guarantee of payment of a court judgment. It is used in small claims court, for example, to assure the payment of the judgment by the losing party, while that party appeals the court's decision. Requiring an appeal bond discourages losing parties from appealing just to avoid paying the judgment.
For example, Sam Smathers loses a case in small claims court and the judgment is $2300. Sam wants to appeal the decision, so he must put up a bond to guarantee that he will pay the $2300, if the appeal fails.