Concise Bible Dictionary:
This was spoken of by the apostle John as then existing. There were many antichrists, whereby it was known that the last time (literally hour) had commenced (1 John 2:18). Apostasy from apostolic doctrine was a sign of the last time (it was not exactly the “last days,” as in 2 Timothy). No further revelation had to be made, and if this doctrine was refused, nothing but judgment could be the result; (Compare 2 Tim. 3:1; 2 Pet. 3:3; Jude 18). The “last days” of Hebrews 1:2 and “last times” of 1 Peter 1:20 are changed by Editors of the Greek Testament to the “end of these days”; These passages refer to the end of the period of the law when the Messiah appeared.
From Anstey’s Doctrinal Definitions:
This expression is used in the New Testament to describe two completely different dealings of God with men. Bible students who do not understand God's dispensational ways with Israel and the Church will be in a quandary when it comes to interpreting the meaning of "the last days." For instance, Scripture indicates that God has visited His earthly people Israel in the "last days" in the Person of His Son (Heb. 1:2), and in those "last times" Christ died and was raised from the dead (1 Peter 1:20-21). Scripture also indicates that Israel will be attacked by the King of the North (Dan. 8:19, 23; 11:40-43) and will be restored and brought into a relationship with the Lord in the "last days" (Dan. 12:1-4; Isa. 2:2-4; Micah 4:1-2). Some of these things have happened 2000 years ago and some of them are yet to happen. The obvious question is: “How can these things all be in the last days?”
People have come up with all sorts of ideas in an attempt to explain this. However, when we understand that the calling of the Church by the gospel is an interposed, parenthetical thing in the ways of God with Israel, the problem is solved. Taking the time of the Church’s sojourn on earth out of the picture (which has been almost 2000 years), we see that God's dealings with Israel go straight from the time of the Lord's death and resurrection to the 70th week of Daniel (Dan. 9:27), which is the final seven years of their history before Christ appears and restores Israel and establishes His millennial kingdom. In that sense, Christ's death as well as those prophetic events regarding the attack on Israel and the nation’s eventual restoration are really all in Israel's last days.
Between Christ’s death and Israel’s restoration (the present interval), God has turned His attention to calling the Church by the gospel of His grace (Acts 15:14). The Church will remain on earth in the place of testimony until the Lord comes to take it home to heaven at the Rapture. It, too, has its "last days" of testimony on earth. The apostles Paul, Peter, and John, and the Lord’s brother Jude, all speak of it (1 Tim. 4:1; 2 Tim. 3:1; 2 Peter 3:3; 1 John 2:18; Jude 18). We are in these last days now, but we are not in the time of Israel’s last days, because these two different dealings of God which must not be confused.