Cornelius and his household would want to hear more about Jesus Christ. Having Peter stay with them gives them a chance to ask him any further questions they have. It also provides opportunity for further instruction and discipleship. Peter agrees to stay so as to teach and give visible expression to the unity that God has authorized and he has proclaimed.1
48 Et il ordonna qu'ils soient baptisés au nom du Seigneur. Sur quoi ils le prièrent de rester quelques jours auprès d'eux.