Peter has just been describing those who serve and worship their corrupted, sensual appetites (1 Peter 4:3-4).  Such people live for today, without thought for eternity.  They judge the 'weakness' of Christians who refuse to do the same, without reckoning on the strength of the judgement of God.  They are so blind: blind to their own nature and its rebellion against truth, blind to their collusion with Satan's purposes, blind to the righteousness of believers who obey God, and blind to His right to judge the wicked.  They are also blind and deaf to the gospel - the only message by which people may find salvation.
 
So they really do need to hear and believe the gospel.  The preaching, proclamation, sharing, and communicating of the gospel through all the media we have available, is the primary work of the church in the world (Acts 10:42).  It alone provides the clear explanation for godly lives.  Some say that the gospel needs no explanation because it is self-evident in the way Christians live: but the truth is that the gospel is good news – a declaration of why and how sinful people can become forgiven children of God, embraced by their heavenly Father.  To be ashamed of presenting this gospel to a dying world shows how little we love the Saviour who gave everything for our salvation, how little we love our neighbours or care about their eternal destiny (Romans 1:16).   

This verse does not mean that God gives a second chance to dead people (that would be against Jesus' own teaching in Luke 16:19-31).  It means that even the most wicked and perverse (spiritually dead) person, who believes in Jesus, will be saved (Luke 23:40-43).  Their physical death does not cut them off from God's salvation because when Christ returns, both the living believers and those who have died will all be raised to new life with Him (1 Thessalonians 4:14-18).
 
The gospel is a surprise to many.  Wicked people, who trust in the salvation which Jesus offers, will go to heaven, while respectable people, who do not trust in Christ, cannot enter.  The difference between the two is that those who submit to Christ are willing to repent of their sins and receive His grace, but those who proudly assert their own uprightness are as blind as the wilfully immoral (Luke 18:9-14).  So this passage should encourage us to persist in following Jesus, however greatly we have sinned: it also encourages us to preach/speak/share the gospel with those who cannot yet see their need, with the prayer that God will use it to bring them to repentance and faith.