The phrase "(there shall be) weeping and gnashing of teeth" (in the original Greek ὁ κλαυθμὸς καὶ ὁ βρυγμὸς τῶν ὀδόντων) appears seven times in the New Testament as a description on the fate of the unrighteous ones at the conclusion of the age. It is thought to derive from a logion in the hypothetical Q source, which yielded Matthew 8:12 and Luke 13:28. The other five occurrences (Matthew 13:42, Matthew 13:50, Matthew 22:13, Matthew 24:51, and Matthew 25:30) are all within the context of parables and are widely held to be redactional additions by Matthew. (source) Others, however, believe redactional theories of the parables are speculative at best, and offer little explanation as to the meaning of this phrase, and only speculate as to why Matthew and Luke included this apparently familiar saying.

The phrase "gnash the teeth" is found in Acts 7:54, in the story of the stoning of Stephen. The phrase was an expression of anger of the Sanhedrin towards Stephan prior to the stoning.

The phrase is also found as an idiomatic expression in colloquial English.

Look up weeping and wailing and gnashing of teeth in Wiktionary, the free dictionary.

'Gnashing of teeth' is when one grinds one's teeth together. Or to have one's teeth set on edge, or to bite down in pain, anguish, or anger.