'I pray that they will all be one, just as you and I are one—as you are in me, Father, and I am in you. And may they be in us so that the world will believe you sent me.'
This is a recorded incident of Jesus praying to His Father. He is not only praying for the disciples, but for all believers present and in the future. He is asking God His Father to make all the children of God to be one. 'One' here means united in spirit and purpose, just like He and the Father are united in spirit and purpose. Why? So unbelievers will comprehend that God the Father sent Jesus His Son to them for their benefit and their salvation.
This was the entire reason Jesus came to earth and lived among us. It was the only way for God the Father to demonstrate His goodwill towards mankind. How did Jesus show His Father’s love? He taught the scriptures accurately, allowing God’s power to validate His teachings with signs and wonders. He healed the broken hearted and the physically sick, cast out demons, and raised the dead. Jesus rectified everything that was wrong in a person’s life. Most important of all, Jesus demonstrated how to have an affectionate, trusting, and personal relationship with our Heavenly Father.
Jesus is earnestly praying the only solution to winning over mankind in this verse. When we as believers line up our purposes with God’s purposes, in the spirit of love as God loves, then the world will believe that God is our Heavenly Father and that Jesus is His beloved Son.
That’s what father means in this verse.