Our Scripture reading today is John 15:15-17.
Verse 16, "Ye have not chosen me, but I have chosen you, and ordained you, that ye should go and bring forth fruit, and that your fruit should remain: that whatsoever ye shall ask of the Father in my name, he may give it you."
One of the purposes for our being a child of God is to bring forth fruit for His glory.  As we are connected the Vine, there will be plenty of spiritual power to accomplish this task. Ephesians 2:10, "For we are his workmanship, created in Christ Jesus unto good works, which God hath before ordained that we should walk in them."  It is God's will that we walk in good works and bear fruit that remains.
There is a connection made between bearing fruit and prayer.  In order to bear fruit that remained there would need to continue to be direct communication with God the Father.  Jesus wasn't going to be wth His disciples much longer so He was once again teaching them the importance of their relationship with the Father.  He is an always will be the connection between us and the Father.  1 Timothy 2:15, "For there is one God, and one mediator between God and men, the man Christ Jesus;"  Our bearing fruit for His glory starts with asking God in Jesus name to strengthen us to bear the fruit.