Yes, Jesus meant that generation in which He spoke the words. The disciples asked Him when that temple would be torn down (Matt. 24:3).
"`Tell us, when shall these be? and what [is] the sign of thy presence, and of the full end of the age?'" (YLT)
The question was specifically about the prophesy Jesus had just spoken to them about the temple they had pointed out to Him. Everything in Jesus' response was a direct reference to the time that Herodian temple would be destroyed. The disciples recognized that the destruction of that temple would mean the end of the age they were living in, specifically the end of the Mosaic covenant.
So many people like to say that the subject changes in Matt. 24:34, but this is wholly untrue. When Jesus said "this generation" it directly applied to the one in which He and the disciples were living. The demonstrative pronoun "this" concerns things that are close to the speaker. Any other generation would have required the demonstrative pronoun "that".
Confusion is also added because "the end" is misapplied to mean the end of the physical cosmos. But there is no such meaning in scripture. A search of "the end" in prophesy is always associated with the specific time of that prophesy.
In Dan. 12:4, Daniel is told to "seal the book till the time of the end," and that end is specific to that prophesy which began in Dan. 9:24 with the time specified of the 70 sevens, or 490 years. Each "end" in Dan. 12 refers back to the 490 years of that specific prophesy, and no further.
The book was unsealed when Christ accepted it at His ascension in Rev. 5:6-7 which happened in the 1st century AD (Acts. 1:9). Daniel asks when the end of these wonders will be (Dan. 12:6), and the answer is
"...`After a time, times, and a half, and at the completion of the scattering of the power of the holy people, finished are all these.': (YLT)
A time, times, and a half was 3-1/2 years, or 1260 days, or 42 months, and ties to the prophesy of the destruction of Jerusalem in Rev. 11:2, 13:5. The holy people of this prophesy was established in Dan. 9:24 as Daniel's people, and Daniel's holy city - the Jews and Jerusalem. The prophesy did not apply to any other people or city than Jerusalem.
The power of the Jews was scattered (or shattered) when that Herodian temple was destroyed by the Romans in AD 70. Therefore, the end of days of Dan. 12:13 was when that temple was destroyed in AD 70.
The prophesy had nothing to do with the end of the physical cosmos. So, knowing that the end of Dan. 12 referred to the destruction of Jerusalem and that Mosaic temple, then when did Daniel stand in his lot? And the answer is after that temple was destroyed when Jesus told His disciples in Matt. 25, which is still the prophesy of the destruction of the temple from Matt. 24, that He would separate out all those from Hades, the sheep to His right and the goats to His left.
"31 `And whenever the Son of Man may come in his glory, and all the holy messengers with him, then he shall sit upon a throne of his glory; 32 and gathered together before him shall be all the nations, and he shall separate them from one another, as the shepherd doth separate the sheep from the goats,
33 and he shall set the sheep indeed on his right hand, and the goats on the left. 34 `Then shall the king say to those on his right hand, Come ye, the blessed of my Father, inherit the reign that hath been prepared for you from the foundation of the world;" (YLT)
Jesus came in His glory at the destruction of that temple in Jerusalem, which is the subject of the entire prophesy of Revelation which is John's Olivet discourse. After Jesus sat in judgment and removed those from the prison of Hades in AD 70, which ties to Rev. 20:11-12, He then threw Hades into the lake of fire (Rev. 20:14).
No one goes to Hades anymore. Every man and woman is judged at their bodily death, as they always have been.
"and as it is laid up to men once to die, and after this -- judgment,"(Heb. 9:27, YLT)
Carefully read the account of Lazarus and the rich man in Luke 16:20-31. Lazarus was judged worth of Abraham's Bosom, or Paradise at his death, but the rich man was judged unworthy and sent into the place of torment at his death. After the temple was destroyed, and Jesus removed all of the souls from Hades, the process changed to an on-going resurrection.
"And I heard a voice out of the heaven saying to me, Write: Happy are the dead who in the Lord are dying from this time!' Yes, (saith the Spirit,) That they may rest from their labours -- and their works do follow them!'" (Rev. 14:13, YLT)
Tell me how anyone would die from that time if Revelation was about the end of the world. Those who died / die in the Lord from that time onward are resurrected, changed in a twinkling of the eye and gathered home to heaven to be with all those righteous souls that have gone before us.
This generation of Matt. 24 was that generation of the 1st century AD. As no other generation ever saw Christ's first manifestation, then no other generation than that one of the 1st century AD could possibly have a 2nd appearance of Him (Heb. 9:28).
Jesus meant what He said, and those who misapply this prophesy to a concept of an end of time and end of the physical cosmos are denying His very words.
Prophesy must be kept in context, and it is very important to recognize the metaphors of God's prophetic language. The Dispensationalists have twisted this prophesy out of all context, and have greatly misled thousands of people. Everything of the prophesy of Matt. 24-25 was completed in AD 70 at the destruction of that temple. Jesus finished the plan of salvation for all mankind, and the gospel message still rings today for all those who will answer His call.
See the following posts at my blog:
Testing The Spirits - Part II: The End ShreddingTheVeil
Testing The Spirits - Part III: Daniel's Lot here
The Signs of Revelation - Part I: The Time of His Coming here
Frequent Mistakes - Part IV: Where Was All the World - here
Frequent Mistakes - Part VI: The End of The World, or ? here