"Gospel": means "the good news", here concerning 'the incarnation, sufferings, and death of Christ', and the salvation through him'; this is basically 'the doctrines of grace, pardon, righteousness, and eternal life'.
"preached": to proclaim it 'openly, freely, and boldly, with faithfulness and consistence'.
"To them that are dead": Theologian John Gill regards "dead" here not in a figurative sense, but "dead in trespasses and sins", as is the case of all mankind or all nations, and is the means of 'quickening dead sinners'. The word "dead" is also used as in the preceding verse, got those who had been alive, but were now dead in a natural sense, whom Christ would judge together with those found alive when he comes; that the Gospel has been preached also to them that are already dead, as well as to those who are now alive.
"That they might be judged according to men in the flesh": may mean, either that such persons who receive and profess the Gospel, and suffer for it, are judged according to the judgment of men that are in the flesh, as in, by the villains, hypocrites and deceivers; and this is the common effect of the Gospel being preached and coming with power to any or the sense is, that such persons, according to men, are judged of God, or have the judgments of God inflicted on them in their flesh or bodies, for some sins of theirs, chastened by the Lord in a fatherly way, that they might not be eternally condemned with the world, or else to complete the sense, for all, who were formerly alive, but now dead, and had embraced and professed the Gospel preached to them, were judged and condemned, and put to death in the flesh by wicked men.
"Live according to God in the Spirit": Although believers were condemned by others while they were here on earth, the Gospel had such an effect upon them, as to cause them to live spiritually, to live by faith on Christ, to live according to the will of God, so though dead in their bodies, they live in their spirits or souls an eternal life of happiness with God, according to his 'eternal purpose, unchangeable covenant, promise, grace, and love'.
Submit to Suffering (4:12–19)
Christians may have to suffer, but they are blessed if it is purely due to their faith, not any criminal or antisocial behavior.
Verse 16
"Christian": This is the third mention of the term in the New Testament—after the first use in Antioch and second mention by Herod Agrippa II —where all three usages are considered to reflect a derisive element referring to the followers of Christ who did not acknowledge the emperor of Rome.