On that day you will realise that I am in my Father, and you are in me, and I am in you.
“On that day” = the day that Christ is resurrected. All of their doubts would be answered and they would know for certain the mutual indwelling of Christ with His Father and with His followers.
“That day” also includes the time between His leaving them and going into heaven and His second coming in our (hopefully) near future. In other words, this is also a promise for you and for me. Every Christian who belongs to Jesus and is seeking after God will know that Jesus is in the Father, we are in Him, and He is in us. These are fundamental truths of Christianity and they only come through experience. Many theologians search the scriptures and debate the divinity of Christ, but the true way of knowing it is to have Him dwell within you. This concept is similar to our gaining knowledge of anything in the physical world except for the knowledge of external facts. For example, you may read poems and books about love and watch movies about it but you will never really understand love until you experience it for yourself.
We can learn a great deal about God by studying His Word, but there are some things that only come through personal experience. Only by dwelling in Him may we truly know that He is divine; only by His indwelling of us may we truly know that He indwells us; and only by our intimate relationship with Jesus can we really know that we are in Him. These are facts that may be gleaned from the Word, but to have them rooted down deep in our innermost being comes only from Him (1 John 5:10, 4:13, Rom 8:16).
1 John 5:10 Anyone who believes in the Son of God has this testimony in his heart. Anyone who does not believe God has made him out to be a liar, because he has not believed the testimony God has given about his Son.
1 John 4:13 We know that we live in him and he in us, because he has given us of his Spirit.
Romans 8:16 The Spirit himself testifies with our spirit that we are God’s children.
What this all boils down to is this: the only way you can know for sure that Christ is who He says He is; that you are saved and belong to Him; and that He lives within you by His Holy Spirit is for you to take Him as your very own Savior and Lord. It is only after you take that step of faith that God rewards you with that certain knowledge.