As explained by Paul in Galatians, he was the apostle to the gentiles where Peter was apostle to the circumcised. This distinction is important because Peter assumes that the audience for his letters knows Scripture and understands the culture and history of Israel. 

• 1 Peter 1, An Imperishable Inheritance
  Peter, writing to Hebrews in the diaspora, starts his letter by explaining that Y'shua is He whom the prophets predicted and that His resurrection is the guarantee of an imperishable inheritance for them. This inheritance is kept in heaven awaiting for revelation 'in the last time.'
• 1 Peter 1-2, Called to Be Holy
  Peter, writing to Hebrews reminds them that they are God's chosen people. As such, they have a duty to conduct themselves in a way befitting that status. This is especially true of Hebrews living in exile among the gentiles.
• 1 Peter 2-3, Authority
  Writing to a minority Hebrew community within a gentile nation, Peter urges them to be respectful of the gentile government. He also urges respect for God's authority structures within their own community and within their families. This is very similar to Jeremiah's message to the exiles in Babylon - You're going to be there for a while, so seek the good of your hosts for your own benefit and peace.
• 1 Peter 3, The Eyes of the Lord
  The Eyes of the Lord are watching to answer the prayers of the righteous, but ignore those of the wicked. The world is a difficult place and there will be abundant opportunities for others to mistreat you. Here Peter reminds his readers of Christ's example; having been reviled and unjustly killed, He acted to forgive and did not curse. Peter also exhorts that we should always be ready to gently explain the reason for our hope.
• 1 Peter 4, The Fiery Trial
  The world is a difficult place in which there are trials and suffering. When the trials are for the sake of your faith, you share in Christ's suffering. This is far better than suffering because you deserve it.
• 1 Peter 5, The Flock of God
  As an elder, Peter exhorts the elders who receive his letter to be faithful in tending God's flock. In this he is echoing Y'shua who gave explicit instructions and dire warnings to those He would leave in charge of His servants. Specifically, He warns them not to use their positions for personal enrichment at the expense of the flock.