What does John 13:36 mean?
In the prior passage, Jesus repeated part of a statement He'd made twice to non-believers in Jerusalem (John 7:34; 8:21). In those comments, Jesus indicated He'd be going where others would seek Him, but be unable to follow, and they'd be unable to find Him. Speaking recently to the disciples, Jesus repeated that He was going where He could not be followed, yet did not indicate these men would fail to find Him (John 13:33).Peter is following up on that statement with his own question. In this context, Jesus' remark implies something much more immediate. And it does—Jesus is about to be arrested and executed (John 19:30), then resurrected (John 20:17) and ascended into heaven (Acts 1:6–9). Those are steps in which His disciples cannot follow, at least not yet.
As Jesus will explain, His path includes preparing a place for those who trust in Him by faith (John 14:3). The disciples, and all who are born again (John 3:3; 3:14–17), will find Christ and be with Him in eternity (John 14:6). The men He has taught for three years cannot do what He is about to do, but they can be reunited with Him eventually.
Another layer of meaning comes when we look at the fates of the men hearing these words. Most of them will suffer martyrdom: killed for their faith in Christ. In that sense, they will "follow afterward" in the path Jesus is about to walk. This includes Peter, who tradition indicates was crucified upside-down, by his own request, as he felt unworthy to die in the same way as Jesus. Peter's eventual fate is even more amazing consider the prediction Jesus is about to give.
John 13:36–38 describes Peter's arrogant claim to loyalty, as a reaction to Jesus' prediction of a secret betrayer. Peter boldly tells Christ he will follow Him anywhere, even to the point of death. Jesus responds with a devastating prediction: Peter will deny his relationship to Jesus three times that very night. Worse, this comment may have made the other disciples suspicious of Peter—they don't yet know that Judas is the betrayer, so this comment might lead them to think Peter is the traitor. Jesus will continue in the following passages with an extended statement of comfort and grace.
Jesus meets with a smaller group, possibly only the twelve disciples, in a private setting. Before eating a meal, Jesus performs the work of a lowly servant, washing the feet of the disciples. He explains that this is an object lesson. Their Lord is willing to serve in humility, so they are obligated to do the same. Jesus also predicts His impending betrayal, subtly telling Judas to leave and complete His conspiracy. The disciples don't realize what's happened, however. Peter foolishly brags about his loyalty. Jesus responds with a cutting prediction: Peter will deny his relationship to Christ three times in the next few hours.