One of the key texts regarding hell is Revelation 21:8, which states:
But the fearful, and
unbelieving, and
the abominable, and
murderers, and
whoremongers, and
sorcerers, and
idolaters, and
all liars,
shall have their part (τὸ μέρος αὐτῶν) in the lake which burneth with fire and brimstone: which is the second death.
Some folks commenting on this verse are quick to rush past "their part," and just act as though the various folks mentioned are just thrown into the fire, like one might through ingredients into a soup.
On the other hand, the word translated "part" has in mind something closer to a geographic area. This is not like our English "take part in," meaning "have a role in." It's more like having a portion or an allotment, or in the real estate sense, a lot.
In context, the portion of these wicked is in contrast to Revelation 20:6
Blessed and holy is he that hath part (μέρος) in the first resurrection: on such the second death hath no power, but they shall be priests of God and of Christ, and shall reign with him a thousand years.
Recall that Christ went to prepare a place for us (John 14:2-3).
Likewise, Revelation 19:22 uses the word to describe a place in the tree of life (or book of life, if you follow the KJV reading there). Revelation 16:19 uses the word to describe that Babylon is carved up into three parts.
Matthew, the gospel with the greatest focus on hell, uses the word in connection with hell:
Matthew 24:51 And shall cut him asunder, and appoint him his portion (τὸ μέρος αὐτοῦ) with the hypocrites: there shall be weeping and gnashing of teeth.
Matthew similarly uses the term as a geographic designator in Matthew 2:22 ("parts of Galilee"), 15:21 ("coasts of Tyre and Sidon"), 16:13 ("coasts of Caesarea Philippi").
Luke does the same in the parallel to Matthew 24:51:
Luke 12:46 The lord of that servant will come in a day when he looketh not for him, and at an hour when he is not aware, and will cut him in sunder, and will appoint him his portion (τὸ μέρος αὐτοῦ) with the unbelievers.
Luke doesn't use the term geographically in Luke (though Mark does at Mark 8:10 "parts of Dalmanutha"), but Luke uses the term of divided portions in Luke 11:36 ("no part dark" of your body), 15:12 ("portion of goods" requested by the prodigal son), and 24:42 ("piece of a broiled fish" given to Jesus after his resurrection). Luke uses the term geographically in Acts 2:10 ("parts of Libya about Cyrene"), 19:1 ("upper coasts" passed on the way to Ephesus), 20:2 ("those parts" he passed over on the way to Greece). Luke also uses the term to describe parts of the crowd (part Sadducees and part Pharisees) in Acts 23:6 and 9. The idol-makers used the term to describe their profession in Acts 19:27. Finally, Luke also uses it to describe the part of the sale of land that was kept back by Ananias and Sapphira (Acts 5:2).
In John 13:8 Jesus tells Peter that he doesn't have a part with Jesus if Jesus doesn't wash his feet. John also uses this word to describe the parts of Jesus garments that the soldiers took for themselves (John 19:23) and the right side of the ship (John 21:6) that Jesus told Peter and the others to fish on after the resurrection.
Paul uses the term to refer to the grave ("the lower parts of the earth") in Ephesians 4:9. Paul also uses the term in a variety of other ways, usually in the sense of something being partial rather than complete or according to some defined partitioning (Romans 11:25, 15:15&24, 1 Corinthians 11:18, 12:27, 13:9-10&12, 14:27, 2 Corinthians 1:14, 2:5, and Ephesians 4:16). In a few places, Paul uses the term to mean something like "in regard to," (2 Corinthians 3:10, 9:3, and Colossians 2:16) which we could equate to something like "about this part." Peter uses the word that same way in 1 Peter 4:16.
The author of Hebrews uses the term to refer to the details of the temple (Hebrews 9:5).
In short, the word can have a range of meanings, but the general sense is one of a part, portion, or the like. The point is that the lake of fire is the destination of the wicked. The righteous have a place in the tree (or book) of life, but the wicked have place in a lake of fire.
Yes, the lake of fire is a metaphor for a place of pain and suffering. The point, however, is that this is where the wicked are going.