In "God's Word for Today" Gordon Snider writes:

While it has become common, especially in Christian songs, to use the phrase “strangers and pilgrims” to describe the spiritual condition of Christians, Peter was likely using that phrase here to describe the social status of his readers. Because they were Christians, these readers were considered without rights or privileges in Roman society. It is in that context that Peter urged them to live in a manner that God was glorified. Such a life is first marked by godly living in contrast to living according to our natural human desires. Notice that the purpose of godly living is not our own salvation, but the salvation of others.

Source: Building Christian Relationships: Adult Teacher's Insights, page 76.