In the last chapter, Jesus told His disciples He was leaving. Peter clearly understood that this meant that Jesus was going to die. I assume that most of them realized that He was headed to a cross to die, and would return to His Father. Jesus told them this many times before, but the reality of it was pressing hard against them.
They were troubled and did not know what the future held. Jesus tells them not to be afraid, He would be with them in the Holy Spirit and that God the Father had things covered.
Jesus equates believing in God with believing in Him. Jesus is the image of the invisible God. He is the revelation of God's glory and the exact substance of God's nature. As they trusted God, they can trust in Jesus. This is the comfort that they have.
The word "believe" (πιστεύετε) is in the present active 2nd person imperative mood. IT IS A COMMAND TO KEEP BELIEVING, AND CONTINUE TO BELIEVE. It is not "you believe in God/Jesus" or acknowledging that you are believing in God. It is more like this; COMMAND: "Continue to believe (Trust) in God, and Trust in Me"
Jesus knew that their faith was going to be shaken. In essence, He was urging them:"Don't lose your faith. Don't let it be shaken. As you have in the past, keep believing and trusting in Me, even though you can't understand what is happening. Keep believing and Trusting that God is in control. It is going to look real bad, but hang in there. The sun will rise again. The Son of God will rise again."
PUTTING IT TOGETHER:Don't be troubled in your heart by what is going to happen. Everything will work out fine in the end. Keep trusting in God, and Keep trusting in Me.