The context of the first six verses aids our understanding. 

1 Peter 4:1-6 (NASB), “Therefore, since Christ has suffered in the flesh, arm yourselves also with the same purpose, because he who has suffered in the flesh has ceased from sin,  so as to live the rest of the time in the flesh no longer for the lusts of men, but for the will of God.  For the time already past is sufficient for you to have carried out the desire of the Gentiles, having pursued a course of sensuality, lusts, drunkenness, carousing, drinking parties and abominable idolatries.  In all this, they are surprised that you do not run with them into the same excesses of dissipation, and they malign you; but they will give account to Him who is ready to judge the living and the dead. For the gospel has for this purpose been preached even to those who are dead, that though they are judged in the flesh as men, they may live in the spirit according to the will of God.”

The text indicates that the “living” and the “dead” are showing the two-fold life of a true follower of Christ. It shows that once their hearts are given to God in full dedication, their desires and goals will have changed. They desire God and His will, spiritual things – rather than earthly, fleshly things. So, they are “dead” to sin (Romans 6:11) and its interests, desires, the things of this world. However, they are “alive” through Christ, living “not after the flesh but after the Spirit.” (Romans 8:5-8) This “judgment” demonstrates that they are no longer viewed by God as a sinful human being, even though by all appearances they are human or flesh. But they are covered by Christ’s blood (1 John 1:7) and are now developing the fruits and graces of the Holy Spirit. (Galatians 5:22-25) 

There is only one Gospel in the Bible. It is the good news that Jesus has died to redeem all mankind. However, presently, it is preached to “call out a people for his name,” Acts 15:14. His name is Christ, and it means anointed. Faithful Christians anointed with the holy spirit will be wed to Jesus Christ in the resurrection. We are receiving judgment now as prospective members of the church class. 1 Peter 4:17 (ASV), “the time is come for judgment to begin at the house of God.” 

During Christ’s second advent, the whole world will learn righteousness (Isaiah 26:9). Yes, “the rest of mankind may seek the Lord,” Acts 14:17 (NASB). This blessed 1,000 year judgment day will be a period of restoration of all that was lost when Adam sinned (Acts 3:19-21). Then the knowledge of the Lord will fill the earth! (See Jeremiah 31:34, Isaiah 11:9)