Summary: No, this is not a reference to hell. Jesus used this expression seven times, and each time it symbolizes the deep regret of great loss – not eternal torture.

  1. In the Parable of the Closed Door (Luke 13:22-308) and the healing for the faithful centurion (Matthew 8:10-13), we learn the Jewish nation was called to accept Jesus as their Messiah but didn’t respond. At Jesus’ first advent, they were given an exclusive invitation to become part of his church. Their inaction opened the door for the Gentiles to follow.
     
  2. In the Parable of the Wedding Banquet (Matthew 22:1-14) and Parable of the Talents (Matthew 25:14-30), we learn that every Christian in the last 2,000 years has had to either individually move forward and follow Jesus or be shown as unfaithful. The weeping and gnashing of teeth consequence applies to them as well.
     
  3. As shown in the Parable of the Wheat and Tares (Matthew 13:24-43, and as described in greater detail below), and the Parable of the Dragnet (Matthew 13:47-50), we learn that false systems of Christianity will be destroyed at the end of the age of the gospel message going out. Systems are destroyed to make way for God’s righteous kingdom, not individuals.
     
  4. With Jesus’ prophecy of his return (Matthew 24:44-51), we see individual challenges to those who are given great responsibility, especially with Christian leadership.

No torture – just great loss and regret.

In the Parable of the Wheat and Tares as referenced in this question, the phrase “weeping and gnashing of teeth” refers to the period of intense anarchy during Armageddon that will cause great suffering and destroy all evilness on earth in preparation for Christ’s righteous reign on earth.

Discussion: Matthew 13:40-44 (KJV), “As therefore the tares are gathered and burned in the fire; so shall it be in the end of this world. The son of man shall send forth his angels, and they shall gather out of his kingdom all things that offend, and them which do iniquity; and shall cast them into a furnace of fire: there shall be wailing and gnashing of teeth. Then shall the righteous shine forth as the sun in the kingdom of their Father. Who hath ears to hear, let him hear.”

Evilness vexes true Christians. Jesus said the gospel would cause fire symbolizing great suffering and even death. I came to send fire on the earth, and how I wish it were already kindled! … 51 Do you suppose that I came to give peace on earth? I tell you, not at all, but rather division” (Luke 12:49,51). History records that believers were tortured, starved, and whole cities massacred during the Dark Ages. Truly, “… men loved darkness rather than light, because their deeds were evil (John 3:19 KJV).

Believers must suffer to learn obedience, as did Jesus.  “…though he was a son, yet he learned obedience by the things which he suffered Hebrews 5:8 (NKJV).  

Jesus said in Mark 9:49, “For every one shall be salted with fire…” This verse explains that all Christians need to be purified through fiery trials. Our consecration vows entail some serious sacrifices to show the depth of our consecration. (See also 1 Corinthians 3:13.) Lastly, Peter 1:7 NKJV, “…your faith, …though it is tested by fire, may be found to praise, honor, and glory at the revelation of Jesus Christ.”

However, Matthew 13:42 is referring to the final suffering and destruction at the end of the present evil world (Galatians 1:4). Daniel prophesied, “And at that time shall Michael stand up, and there shall be a time of trouble, such as never was since there was a nation even to that same time…” – Daniel 12:1 KJV Jesus also said, “For then there will be great tribulation, such as has not been since the beginning of the world until this time, no, nor ever shall be…” (Matthew 24:21-22 NKJV).

Malachi 4:1, “For behold, the day is coming, burning like a furnace; and all the arrogant
and every evildoer will be chaff; and the day that is coming will set them ablaze, says the LORD
of hosts, so that it will leave them neither root nor branch.” 

Note the reference back to the “furnace of fire” described in Matthew 13:42.

Mankind longs for justice, righteousness and peace. The purpose of the fiery suffering is to humble men’s hearts. Then Christ will step in and establish his righteous reign. “They shall not hurt nor destroy in all My holy mountain, for the earth shall be full of the knowledge of the LORD as the waters cover the sea” (Isaiah 11:9 NKJV).

Additional Resources:
There are many scriptural details on this important topic. Here are recommended study helps.

Free PDF: “The Truth About Hell”

Christian Questions Podcast 
Episode #1342: “What Does “Weeping and Gnashing of Teeth” Mean? (Hellfire Series Part II)”
Learning what Jesus meant by “weeping and gnashing of teeth”
CQ Rewind Show Notes

Episode #1006: “Has the Gospel Been Corrupted? (Part I)”
The present-day lessons from the Wheat and Tares Parable
Preview Video
CQ Rewind Show Notes

Video: What does the Parable of the Wheat and Tares mean?