The meal they were sharing was the Passover meal. There is a ceremony near the beginning of the Passover where participants engage in a hand-washing ceremony. We believe that this foot-washing took place at this point in the meal.
When Jesus took off his outer garment and wrapped the towel around his waist he was dressed like every other slave dressed, and the disciples would've recognized this fact.
Foot washing was one of the most unpleasant chores you could possibly do in those days. In fact, I once read that if you were a Jew and you owned a Gentile slave and a Jewish slave, you would never ask your Jewish slave to wash feet - unless you really wanted to punish him.
So, when Jesus puts on the clothing of a slave and begins to do the very dirty job of washing feet, it set the disciples back, as you can see if you read the entire passage in John 13.
After Jesus washed their feet - even the feet of Judas - he puts back on his outer robe and says:
First of all, every follower of Jesus is commanded to love: “A new command I give you: Love one another. As I have loved you, so you must love one another.” (John 13:34)
Secondly, loving one another means serving one another: “You, my brothers and sisters, were called to be free, (therefore)…serve one another humbly in love. For the entire law is fulfilled in keeping this one command: “Love your neighbor as yourself.” (Galatians 5:13-14)
Third, those who are leaders in the Church must be servants: “The greatest among you will be your servant. For those who exalt themselves will be humbled, and those who humble themselves will be exalted.” (Matthew 23:11-12)
Therefore, if every Christian is called to be a servant, and if loving one another means serving one another, and if those who serve others are leaders in the Body of Christ, then every Christian is a leader.
That means Christianity is for leaders only.
So, the more we serve others in the Body of Christ, the greater we become. The greater we become the more authority we are given to serve others. The more we exercise our authority to serve by serving more people, the greater servants we become, and the greater we become in the Kingdom. It’s really very simple.
Those of us who are leaders in the church (and that’s all of us) are called to be just like Jesus, and even Jesus “did not come to be served, but to serve and to give his life” for others. Paul the Apostle follows up these thoughts by pointing out that everyone in the Body of Christ is called to love – and to serve – everyone else. In short, everyone who calls themselves a Christian is, in fact, a servant, and therefore, a leader. This means that Christianity is for leaders only.
"In your relationships with one another, have the same mindset as Christ Jesus: Who, being in very nature God, did not consider equality with God something to be used to his own advantage; rather, he made himself nothing by taking the very nature of a servant, being made in human likeness. And being found in appearance as a man, he humbled himself by becoming obedient to death — even death on a cross!" (Philippians 2:5-8)