Peter once told Jesus that he would go with Him even to the point of death. Jesus responded by telling His well-intentioned disciple that not only would he not follow through on that, but how he would falter, how many times and within what very specific time frame. Luke 22:61 tells us that as soon as Peter denied that he even knew Jesus for the third time that the rooster crowed "and the Lord turned and looked at Peter".
Now, as rough as all of that must have been for Peter, I don't believe that Jesus said those things and looked at Peter just to hurt him. Once Jesus' work on the cross was done, I believe, that it all made sense to Peter. The humbling correction of Peter's statement and the moment of eye contact serve to let Peter know, and by extension all of us, that Jesus, knowing what Peter was going to do, still willingly went through the horrors that He was about to endure.
We need to always remember that Jesus did what He did knowing you and knowing me. He knew those moments when my best intentions would fall. He had already seen the times when my strength would fail. Peter just happened to be the one who was there to receive the look from Jesus on our behalf. The look said to us: "I know everything; now watch what I'm going to do anyway."