After Jesus got arrested, Peter wanted to keep himself at a distance from Jesus. It's likely that fear of reputation is a factor. Peter even denied his connection with Jesus towards a servant girl.
But even more people (including a servant of the high priest) asked Peter about being a disciple to Jesus, and Peter denied Jesus again. Outside pressure continued, resulting in the continuation of Peter's attitude. Altogether Peter denied Jesus three times, and at that time, the rooster crowed.
These events are basically what Jesus said would happen back in John 13. Jesus knew that Peter's heart focused on being good with the public and wouldn't fare well with Jesus's arrest and the resulting implications. But Jesus isn't done with Peter yet -- even after the arrest.