What does John 20:6 mean?
Peter arrives at the tomb after John (John 20:1–4), but he is the first to walk in. John is waiting near the entrance, either out of fear or respect (John 20:5). This corresponds to Peter's typical enthusiasm (Matthew 14:28–29; 26:35; John 18:10).Jesus was buried quickly (John 19:42), but Nicodemus and Joseph still wrapped His body before closing the tomb (John 19:39–40). Mary Magdalene had reported that the body was gone—and yet the grave clothes are still there. That would have been confusing, to say the least. One can imagine both Peter and John wondering why someone would unwrap the corpse before stealing it.
In context with the following verse, it seems likely Peter is speaking to John about what he sees. A crucial detail is one of the cloth pieces. This was, somehow, identifiable as the one used specifically for a person's face (John 11:44). Peter notes that it's not with the rest of the remnants. John will come in to see this for himself and have a moment of realization (John 20:7–8).
In hindsight, the presence of the grave clothes helps explain something about Jesus' resurrection. When Lazarus was raised, he was still bound in his burial linens (John 11:44). Jesus was also wrapped, but those strips are still here—the body is gone. The implication is as if Christ passed right through the clothes. Later, Jesus will come through a locked door to speak with the disciples (John 20:19). He will repeat the action to see Thomas (John 20:26).
This raises the question of why the stone was rolled back—if Jesus could pass through solid matter, why open the tomb? The answer, it seems, comes in this very passage. This is visual, physical evidence meant to be seen and understood.