What does “under the earth” mean?

Answer:

We typically refer to heaven as being located "up," even though it isn't in this physical universe. Since we bury the dead, it is common to refer to the realm of the dead as "down."

"Now this expression, 'He ascended,' what does it mean except that He also had descended into the lower parts of the earth? He who descended is Himself also He who ascended far above all the heavens, so that He might fill all things" (Ephesians 4:9-10).

Paul is discussing how Jesus descended from heaven to earth, then to the grave at his death, from which he was raised and ascended to heaven.

In Philippians 2:10, Paul is stating that Jesus rules everything (Matthew 28:19). He rules in heaven. He rules the earth. He rules even the realm of the dead. "Do not marvel at this; for an hour is coming, in which all who are in the tombs will hear His voice, and will come forth; those who did the good deeds to a resurrection of life, those who committed the evil deeds to a resurrection of judgment" (John 5:28-29).

Another verse has a similar phrase. "And no one in heaven or on the earth or under the earth was able to open the book or to look into it. ... And every created thing which is in heaven and on the earth and under the earth and on the sea, and all things in them, I heard saying, 'To Him who sits on the throne, and to the Lamb, be blessing and honor and glory and dominion forever and ever'" (Revelation 5:3, 13).