It is a central tenet of Scripture that there will be a final judgment. The day will come when all men and women and children will stand before the Judge. Scripture frequently mentions judgment in connection with resurrection, which is a solemn reminder that not even death can prevent our coming before the Judge.
Acts 17 relates the story of the Apostle Paul's addressing the Athenians. He told them:
God therefore, having overlooked the times of ignorance, now enjoins men that they shall all everywhere repent, because he has set a day in which he is going to judge the habitable earth in righteousness by [the] man whom he has appointed, giving the proof [of it] to all [in] having raised him from among [the] dead.
There are several noteworthy points in these two short verses. First, the whole world is heading towards judgment. God has been extremely patient with the world: He has "overlooked the times of ignorance". But God has set a day when the whole world will be judged. We don't know exactly which day, but God has chosen a day, and on that day there will be judgment on the whole world.
Further, the Judge will be a Man. This is a very important point. Our Judge knows exactly what it's like to live down here. He knows what it's like to be hungry and thirsty and tired and alone. He won't be convinced by "But you don't understand!" He knows exactly what this wicked world is like: He lived in it.
More than that, God has publicly demonstrated which Man He has chosen as Judge by raising Him from the dead. When God raised Christ Jesus from the dead, He was doing so as a declaration that Christ Jesus was going to be the Judge of all men.
God hasn't told us this for no purpose: there is a reason that He has told us judgment is coming, there is a reason He has shown us whom He has appointed to be our Judge. The reason is in v. 30, He "now enjoins men that they shall all everywhere repent". God has told us judgement is coming because He wants us to repent. He's given us the Resurrection as a warning. And He's told us exactly who our Judge is going to be so that we'd know to Whom we should repent.
The Lord Jesus, when He was on the earth warned the people of His day that He would be their Judge. More than that, He told them precisely what they should do as a result of that:
22 for neither does the Father judge any one, but has given all judgment to the Son; 23 that all may honour the Son, even as they honour the Father. He who honours not the Son, honours not the Father who has sent him.
24 Verily, verily, I say unto you, that he that hears my word, and believes him that has sent me, has life eternal, and does not come into judgment, but is passed out of death into life.
The Lord Jesus warned the people that it's not the Father who'll judge us, it's the Son. And the Father's purpose in appointing the Son as our Judge is so that we'd "honour the Son, even as they honour the Father" (v. 23).
The Lord Jesus then went on to point out that there is one certain escape from the coming judgment: hearing His words and believing on the Father who sent Him (v. 24).
So here again, we find that the Lord Jesus Christ is the Judge of all men. And it is God's explicit desire for Him to be the Judge, because He wants everyone to honour the Lord Jesus as God.
The Lord Jesus went on to explain:
26 For even as the Father has life in himself, so he has given to the Son also to have life in himself, 27 and has given him authority to execute judgment [also], because he is Son of man.
28 Wonder not at this, for an hour is coming in which all who are in the tombs shall hear his voice, 29 and shall go forth; those that have practised good, to resurrection of life, and those that have done evil, to resurrection of judgment.
There are two resurrections coming: the Son of God is going to raise the dead for the "resurrection of life", or for the "resurrection of judgment". Here they sound like they're at the same time, but Revelation 20 puts them 1000 years apart (cf. Revelation 20:4–5).
Notice this is what the Lord Jesus was warning about just a couple verses earlier. There is a judgment coming, and no one can escape it. If you die before judgment, that's not going to stop Him: He'll just raise you from the dead. This is the only appointment no one can miss.
We notice a strange expression in v. 27, the Lord Jesus is the appointed Judge because He is the Son of Man. That might sound strange to us: we might expect Him to be the Judge because He is the Son of God. Or perhaps even because He is the Son.
Why does the Son of Man get to judge?
The answer is all the way back in Genesis. God gave man dominion over the whole earth (cf. Genesis 1:26–30). What did man do with it? He plunged the whole creation into sin. God has given dominion to man as a race, and to specific men as individuals: Adam (Genesis 1:26–30), Noah (Genesis 9:1–8), and Nebuchadnezzar (Jeremiah 27:5–8). In every single case, the men to whom God has entrusted dominion were totally unworthy of it. Nothing but disaster has come from it.
But God's no cheat. He has put man in charge, and He doesn't simply take away dominion when it doesn't work out well. So God, having tried various men, has had to supply His own Man: the Son of Man. It is God's intention that this Man would take the final dominion.
1 Corinthians 15 looks forward to when Christ Jesus will give up dominion to the Father. That day is coming too. But first He's going to subdue all things, and that means the Son of Man will be the Judge.