John 14:1 Let not your heart be troubled: ye believe in God, believe also in me.
John 14:27 Peace I leave with you, my peace I give unto you: not as the world giveth, give I unto you. Let not your heart be troubled, neither let it be afraid.
When Jesus spoke these words to His disciples, the disciples were about to face the biggest change of their lives. The disciples had been traveling with Jesus for about three years at that point. They had abandoned their lives and livelihoods and walked across the country with Jesus. They had heard His teachings, seen miracles performed, and come to understand that Jesus was the long awaited messiah. They probably thought that the calling of Jesus was the biggest change they would ever experience in their lives. But, bigger changes were yet to come.
Jesus had just explained to them that He would have to leave them and you can tell from the questions of Peter, Thomas and Phillip that Jesus' statements about going away were confusing. "Where are you going?" Peter asked. It is in this context that Jesus reassures them. Jesus says, "Things are going to change, but don't let it trouble you." He then gives them the knowledge they need to handle this momentous change that is about to occur.
First and foremost is faith in God and Jesus. Jesus acknowledges their faith in God and then tells them to have that same faith in Himself. In effect, He said "you already have directed your faith towards God, now also direct the same faith towards Me." By doing so, Jesus establishes without any doubt that He has the power of the Father, and that anyone who comes to Him comes to God. Jesus goes on to explain in succeeding verse that the only way to come to God is through Jesus himself.
This is always the response that we should have when faced with momentous change. Do not be troubled, but trust in the Lord. That trust is what gets us going in the right direction when everything seems to be turned around. But, Jesus gives them a promise beyond that -- a promise that is unique in all of history. He tells them that, although He is leaving to return to the Father, He will send His spirit to them to comfort and guide them from then on. This is not something the world can see or receive. It is a gift from our Lord, for our faith, that gives us the wherewithal to face any change, any challenge, that the world may hurl at us. For that reason, we have no need to fear. We have the peace of our Lord always no matter how things change.