Jesus speaks against the Pharisees and scribes of his day in Matthew 23.
31 Thus you testify against yourselves that you are descendants of those who murdered the prophets. 32 Fill up, then, the measure of your ancestors. 33 You snakes, you brood of vipers! How can you escape the judgement of Gehenna? 34 Therefore I send you prophets, sages, and scribes, some of whom you will kill and crucify, and some you will flog in your synagogues and pursue from town to town, 35 so that upon you may come all the righteous blood shed on earth, from the blood of righteous Abel to the blood of Zechariah son of Barachiah, whom you murdered between the sanctuary and the altar. 36 Truly I tell you, all this will come upon this generation.
The most straightforward reading of this passage identifies Gehenna with the punishment "this generation" will soon receive for shedding the blood of the righteous. There is no good reason to distinguish between "the judgement of Gehenna" and the blood vengeance that will come upon "this generation." They are interchangeable.
What is suffered by "this generation" is always an eschatological day of judgement over the earth (cf. Matthew 12:41-42, 16:28, 24:34). "This generation" is never said to suffer a postmortem punishment. The point Jesus is making in the "this generation" passages is that the kingdom and judgement are rapidly entering into history.
Jesus continues:
37 “Jerusalem, Jerusalem, the city that kills the prophets and stones those who are sent to it! How often have I desired to gather your children together as a hen gathers her brood under her wings, and you were not willing! 38 See, your house is left to you, desolate. 39 For I tell you, you will not see me again until you say, ‘Blessed is the one who comes in the name of the Lord.’”
The desolation of Jerusalem's house is an obvious reference to the destruction of the Temple in AD 70. The "sacrilege of desolation" set up in the Temple will signal the impending desolation of Jerusalem (Matthew 24:1-2; 15-18, Luke 21:20-28).
Jesus has here given another explanation as to what the judgement of Gehenna is. It is both blood vengeance for killing the prophets (23:35) and the desolation of Jerusalem for repeatedly spurning Jesus (23:38, cf. Matthew 22:7).
Gehenna therefore refers to the coming destruction of Jerusalem by Roman armies.
How could this be?
1. The word Gehenna is appropriated from the oracles of Jeremiah which claimed that the valley of Hinnom near Jerusalem (Hebrew: Ge Hinnom, Aramaic: Gēhannā) would become the valley of Slaughter when Babylonian armies destroyed the city in 586 BC (Jeremiah 7:30-34, 19:4-6). The image of Gehenna therefore originates in reference to a military catastrophe that befell Jerusalem and its Temple. It would have been a suitable metaphor to describe what occurred in AD 70.
2. Jesus appeals to Isaiah 66:24 in his most detailed description of Gehenna: it is "where their worm never dies, and the fire is never quenched." This language naturally depicts the status of bodies disposed of after a successful siege. Such corpses are piled up without burial. They are eaten by worms and burned. This interpretation is confirmed by the context provided by Isaiah 66:24 which says that the inhabitants of a restored Jerusalem will go out to see the bodies of those who rebelled against YHWH and were subsequently slaughtered (Isaiah 66:16). What Isaiah 66 describes then relates to the land of the living, not to the afterlife. Living human beings cannot go out and see those who are now in a postmortem Hell. Thus this text too indicates that Gehenna is a place of earthly slaughter and inadequate burial.