In Greek mythology, Tartarus was the lowest hell, the place where the Titans (who were defeated by Zeus) were restrained. It is described as being as far below Hades as heaven is high above the earth. As far as we can apply Greek mythology, we can understand that these angels were cast so far down as to be out of sight. Their place of restraint was so far down that one would think they would never be able to crawl out.
God is trying to get across that the angels have been defeated—cast down from heaven to the earth, as Revelation 12 shows. The earth, then, is a place of restraint, a prison, for them.
To add to the imagery, they are bound in "chains of darkness." This amplifies the thought that Peter is making: The demons are restrained. There is some disagreement among scholars whether Peter uses the word that is translated here as "chains" or whether he means "silo." Almost everyone understands what a silo is. To an American, it is a tall, cylindrical object in which grain is stored. To the Greek, a silo was an underground pit where grain was stored. Whether it is a chain or a silo, it does not matter. God is trying to assure us that the demons have been restrained.
They are being restrained because they are facing judgment. Unfortunately for us, they are restrained in the place where we live! The earth is the silo, the storage bin. We are sharing this place with them. Worse, as they would see it, we are intruders in their space. They consider us invaders.