Peter's argument in the section of 1 Peter from which the verse is taken is basically this: Suffering is inevitable in this world. It's an imperfect, sinful place, after all. Christians may, in fact, experience suffering they wouldn't otherwise undergo because they are Christians. The message that Christians bear, that the suffering Savior Jesus calls all people to surrender to Him because He is the only way to rightness with God, offends most of the people of the world.
But, Peter says, whatever suffering you may endure, keep glorifying the God Whose Son died and rose for you. Jesus Christ deserves our unreserved allegiance and total devotion!
Check out today's installment of Our Daily Bread.