What does John 13:13 mean?

Washing of feet was a dirty, lowly task. In Jesus' era, this was always done by someone of lower status for someone of higher status. This is why Peter's first reaction was to absolutely refuse such a gesture (John 13:6–8).

In this statement, Jesus clarifies that He is not denying His role as their Lord. In fact, He is emphasizing it. Despite what Peter may have thought, Jesus is in no way putting Himself on the same level as the disciples. Rather, He's doing the opposite. Washing their feet was not meant to contradict the idea of Christ as Master. Instead, it draws a hard line that challenges our normal sense of what leadership means. It also establishes common love and support as fundamental parts of living out the Christian faith.

Jesus will go on to explain that when the Master performs a task, servants don't get to dismiss that same action as "beneath them." In this one moment, Jesus crushes the benchmark of "that's beneath me" all the way to the floor. The greatest of all leaders, Jesus Christ, worked in humility and service to others. No Christian, regardless of status, title, role, or reputation, has a right to turn up their nose at sacrificial service. To do so would be to suggest, absurdly, that such a person is "too good" to do what Christ did.