I think the question of the meaning and timing of the "last day" is a good one, and one that I asked myself several years ago.
John 11:24 Martha saith unto him, I know that he shall rise again in the resurrection at the last day.
Martha, talking to Jesus, tells us exactly what she knew to be true... the last day is the day of the resurrection.
The "last day" as spoken by Jesus in the Gospel of John gets even more interesting when we see that the resurrection is actually split into two resurrections. One at the beginning of the 1000 years and another at the end of it.
Rev 20:4 And I saw thrones, and they sat upon them, and judgment was given unto them: and I saw the souls of them that were beheaded for the witness of Jesus, and for the word of God, and which had not worshipped the beast, neither his image, neither had received his mark upon their foreheads, or in their hands; and they lived and reigned with Christ a thousand years.
The dead in Christ are raised at His coming, and this is the first resurrection:
5 But the rest of the dead lived not again until the thousand years were finished. This is the first resurrection.
Then the rest of the dead are raised at the end to be judged:
Rev 20:6 Blessed and holy is he that hath part 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. 7 And when the thousand years are expired, Satan shall be loosed out of his prison, 8 And shall go out to deceive the nations which are in the four quarters of the earth, Gog and Magog, to gather them together to battle: the number of whom is as the sand of the sea. 9 And they went up on the breadth of the earth, and compassed the camp of the saints about, and the beloved city: and fire came down from God out of heaven, and devoured them. 10 And the devil that deceived them was cast into the lake of fire and brimstone, where the beast and the false prophet are, and shall be tormented day and night for ever and ever. 11 And I saw a great white throne, and him that sat on it, from whose face the earth and the heaven fled away; and there was found no place for them. 12 And I saw the dead, small and great, stand before God; and the books were opened: and another book was opened, which is the book of life: and the dead were judged out of those things which were written in the books, according to their works. 13 And the sea gave up the dead which were in it; and death and hell delivered up the dead which were in them: and they were judged every man according to their works. 14 And death and hell were cast into the lake of fire. This is the second death. 15 And whosoever was not found written in the book of life was cast into the lake of fire.
Notice Jesus talks of two resurrections here:
John 5:29 And shall come forth; they that have done good, unto the resurrection of life; and they that have done evil, unto the resurrection of damnation.
Jesus talks of those who are His being raised on the last day, so this is part of the FIRST resurrection before the 1000 years:
John 6:40 And this is the will of him that sent me, that every one which seeth the Son, and believeth on him, may have everlasting life: and I will raise him up at the last day.
Paul also shows us that at the last trump, the 7th trumpet of Revelation, the dead in Christ shall be raised:
1 Cor 15:51 Behold, I shew you a mystery; We shall not all sleep, but we shall all be changed, 52 In a moment, in the twinkling of an eye, at the last trump: for the trumpet shall sound, and the dead shall be raised incorruptible, and we shall be changed.
1 Thess 4:16 For the Lord himself shall descend from heaven with a shout, with the voice of the archangel, and with the trump of God: and the dead in Christ shall rise first: 17 Then we which are alive and remain shall be caught up together with them in the clouds, to meet the Lord in the air: and so shall we ever be with the Lord.
So, we see that the last day is the day Christ raises His own to be with Him, and that it's before the 1000 year reign, but after the time of the Antichrist when the Mark of the Beast is given (Rev 20 quoted above). It's the day the Lord returns to the earth to gather His people, and then He pours out His wrath on the children of disobedience (Col 3:6).
Joel 2:31 The sun shall be turned into darkness, and the moon into blood, before the great and the terrible day of the LORD come.
The Day of the Lord is both great (He comes to take His people to be with Him), and terrible (He pours out His wrath on the remaining people, the children of disobedience).
If any of this is unclear or you would like more information, I would suggest reading through Book 1 on my web site to really get a handle on the prophecies God foretold of the last days, especially chapters 7 through 10.