In the final moments before the crucifixion, Jesus took time to demonstrate the importance of service. This was also the time where Judas Iscariot, one of Jesus's own disciples, betrayed Jesus.
Before the betrayal, however, Jesus knew what was going on with Judas (since he knows the hearts of the disciples and that the betrayal has the heart locked in). Jesus noted that he knows the disciples and talked about how Scripture would be fulfilled (13:18). The verse in view is part of Psalm 41, which talks about how David is stressed due to witnessing enemies and even betrayers but knows to focus on the Lord. Like David, Jesus also had some stress, especially with knowing that one of the disciples would betray Jesus, but Jesus focused on the Lord. The road to betrayal "fulfills" Scripture in that it measures up to what David describes what betrayed is like. In fact, we know that Jesus is "troubled in spirit" and told the disciples that "one of you will betray [Him]" (13:21).
But even then, Jesus gave the disciples a promise. The one who receives whoever Jesus sends receives Jesus and also receives the sender (13:20). Later on, we'll see Jesus send the Holy Spirit that people who place faith in Jesus receive. He'll also explain the Holy Spirit in the next few chapters.