A counteroffer is a response to an initial offer in negotiations, where the original offer is rejected and a new offer is proposed instead. This process signifies a willingness to negotiate and can shift the terms of the agreement, reflecting the interests of the responding party. In strategic bargaining scenarios, such as those described in the Rubinstein model, counteroffers play a crucial role in determining the final agreement by influencing the dynamics of power and concessions between the parties involved.