In the days of Jesus's arrest, a few disciples -- including Simon Peter -- followed Jesus for a while. While one of the disciples followed Jesus into the courtyard, Peter stood at a distance. Eventually, Peter got brought in, and after getting asked by a servant girl, Peter denied that he is the disciple of Jesus.
At that time, it's likely that the connection with Jesus and the disciples were discovered. Considering that Jesus is arrested, the association doesn't look good. It's likely that Peter had a fear of reputation in his heart (and also his powerlessness to stop Jesus from getting arrested -- especially with Jesus rebuking Peter after the sword incident). Thus, Peter wanted to distance himself from Jesus, as evident by not only the denial but also the decision to stand outside at a distance.