In my opinion, these verses mark the climax of the book of John. Fear is the primary emotion in the scene: the disciples are huddled together, terrified that the Jews will find them and they will share the same fate as Christ.
Their terror is justified: the Disciples had recently witnessed the brutal crucifixion of the person that they cared for and believed in.
They must have been emotionally conflicted with feelings of sadness, doubt, fear, and guilt. What should they do?
At that moment, Christ appears and says: "Peace be unto you."
I can imagine there were no more beautiful words that the disciples could have heard. Their fears must have been immediately alleviated, and the doubts that they previously held must have been quelled.
This verse has a different meaning for me: when I put myself in the shoes of the Disciples, I am filled with feelings of anger, hate, sadness, guilt, and selfishness in wanting to protect myself. I would be so bitter and filled with doubt about all that I had learned from Jesus while harboring a deep hatred for the Jews.
Jesus comes back to send me a message: "Peace be unto you."

