Mary herself was afraid because she was also sinful. Joseph was afraid, and now the shepherds were afraid, the Greek text says, with great fear. This fear is fear of the divine damnation of death because of our sins. No, this fear of death and damnation can only be eliminated by the gospel. I bring you good news of great joy that will be for all the people.
Great fear is dealt with by the gospel of great joy.
That means in the fullness of time, in fulfillment of God's ancient prophecy and promise. The time had come. This baby was the son of David and heir of his throne. This Jesus was the one who would crush the head of the serpent. He would defeat Satan and demons and every force that is against God and man.