Joshua was his minister or servant, and it would be a satisfaction to him to have him with him as a companion during the six days that he tarried in the mount before God called to him. Joshua was to be his successor, and therefore thus he was honoured before the people, and thus he was prepared by being trained up in communion with God. Joshua was a type of Christ, and (as the learned Bishop Peirson well observes Moses takes him with him into the mount, because without Jesus, in whom are hid all the treasures of wisdom and knowledge, there is no looking into the secrets of heaven, nor approaching the presence of God.
Related Commentaries of Exodus 24:13
Exodus 24:13
13 And Moses rose up, and his minister Joshua: and Moses went up into the mount of God.