What does Matthew 4:20 mean?

Matthew reports that Peter and Andrew did not hesitate for a moment. Andrew, at least, had already served as a disciple under John the Baptist. The brothers believed Jesus to be the Messiah, the promised Christ who would bring the kingdom of heaven to earth. They understood who Jesus was and the role He was giving them as trainees under His leadership.

They apparently did not even pack up their work. They left their nets behind and immediately began to follow Jesus, demonstrating full commitment to whatever path He would lead them on. Their faith in Jesus is remarkable, though they did not yet have any idea what they were getting into.

Some of the men's willingness to immediately follow Jesus, here, is explained by their earlier encounter with Christ (John 1:35–42). This is not a stranger, it's someone they already know, and have good reason to want to follow.