The Idea in Brief
The "Times of the Gentiles" is the period of time when the visible theocratic kingdom on earth is absent. That is, when the visible theocratic kingdom on earth existed, the Biblical referent of time was in reference to what Jewish ruler(s) were in power. When the theocratic kingdom on earth ended with the departure of the glory of the Lord (right before the Babylonian Captivity), the Hebrew Bible then referenced Gentile powers as the referent of time from that point forward. This Gentile rulership began at the time of the Babylonian Captivity, and continues to this day, and therefore the fulfillment of the Times of the Gentiles awaits a future day, when the visible theocratic kingdom will be established again on earth.
In the Hebrew Bible, the theocratic kingdom on earth began at Sinai, when the glory of Yahweh dwelt in the Tabernacle (glory-dwelled = "shekinah") and later in Solomon's Temple. First Moses, the judges, and then the Jewish kings were the divinely-anointed representatives of the leadership of this theocratic kingdom on earth. Before Sinai, God's covenants with man (e.g., Noahic and Abrahamic) the divine revelation was direct and personal; at the Covenant at Sinai, however, was the first formal establishment of the Government of God (theocratic kingdom), through which the nations of the earth would be blessed.
Therefore the referents of time for the theocratic kingdom were not based on the age of the world, but based on the reigns of these respective Jewish leaders at the time. For example, Hebrew Scripture references the reigns of the Jewish kings as time-referents, since they had represented the leadership of the theocratic kingdom (even when divided).
1 Kings 16:23 (NASB)
23 In the thirty-first year of Asa king of Judah, Omri became king over Israel and reigned twelve years; he reigned six years at Tirzah.
The rule of Jewish kings was the basis of gauging time, since their rulership was the executive authority of Yahweh, who was the Head of State of the theocratic kingdom, even if divided. The laws of this kingdom came from the Torah.
However, when the Babylonian Captivity occurred, the glory of Yahweh had departed the Temple and this theocratic kingdom on earth ended: thus the reign of Jewish kings had terminated (and so there was no longer any more referent of time based on the reign of any Jewish kings). At this time the prophet Daniel introduced the images of reigning Gentile powers on earth as rapacious animals, whose power on the earth would one day end. So post-exilic Hebrew Scripture such as Zechariah and Haggai reference the reigns of these Gentile powers (and not Jewish kings) as the time-referents, and so these -- thus "the Times of the Gentiles." The following graph provides an overview of "the Times of the Gentiles."
The last eight chapters of Ezekiel (approximately 20% of the book) concerns dozens of measurements, which suggest the literal establishment of the new temple, where the glory of Yahweh will one day dwell. (The dozens of references to precise measurements with a ruling measuring rod suggest that this temple is literal.) It was in this context of the apocalyptic end that Jesus was alluding in Luke 21:24 to the fulfillment or completion of the "Times of the Gentiles," when Gentile rule would end in the world in general and over the Promised Land in particular. That is, Jesus was alluding to the time when these rapacious Gentile powers would no longer dominate the earth.
At the current time (today) we are living in the invisible kingdom of God (under the New Covenant), where the temple is the body of the believer in the individual and collective sense. That is, the believer operates in the kingdom of God while on earth (please see Acts 26:16-18 and Col 1:13). Since this kingdom is invisible, there is no exercise of direct theocratic authority on earth. That is, there is no direct exercise of the Torah within this invisible kingdom. The beginning of this invisible kingdom was the inauguration of the New Covenant at Pentecost.
On the same day that the New Covenant was given at Pentecost was the same day that the Old Covenant was given at Sinai. Also, the same dates that the Jews escaped Egypt (and when the Egyptian Army was destroyed) are the same dates as the crucifixion and resurrection of Jesus Christ. In other word, the Old Covenant and New Covenant, respectively, were announced publicly to Israel on the same dates on the Jewish calendar in precise coincidence. The only twist for the New Covenant was the revelation of the "Mystery" later revealed to the Apostle Paul, who declared that Jews and Gentiles are now one in the mystical Body of Christ (Eph 3:4-12). This twist of the New Covenant was not part of the Hebrew Scriptures, and the Apostle Paul relates that when the Mystery is over, then Israel will once again become the locus of history for the return of the visible theocratic kingdom on earth.
Rom 11:25-27 (NASB)
25 For I do not want you, brethren, to be uninformed of this mystery—so that you will not be wise in your own estimation—that a partial hardening has happened to Israel until the fullness of the Gentiles has come in; 26 and so all Israel will be saved; just as it is written,
“The Deliverer will come from Zion,
He will remove ungodliness from Jacob.”
27 “This is My covenant with them,
When I take away their sins.”
This Mystery is an intercalation, or heretofore undisclosed interruption, to the divine time table. When Jesus prophesied the destruction of Israel by the Romans in Mark 13, Matthew 24, and Luke 21, the destruction of indeed occurred in AD 70. However, the Second Advent of Jesus Christ did not occur immediately after AD 70 as was expected, because the intercalation of the Mystery (as revealed to the Apostle Paul) had begun after Pentecost when the Gentile Roman Centurion and his Gentile family spontaneously received the Holy Spirit without any intercession or laying of hands by Peter (Acts 10:1-48). The baptism of the Gentiles (Cornelius and his family and cohort) shook the Jewish Christians who alone were the recipients of the national announcement of the New Covenant at Pentecost.
When the intercalary period of the Mystery is over (the rapture discussed by the Apostle Paul in 2 Thess 2:1-16), is when God will reestablish the visible theocratic kingdom on earth again. (The literal temple described in the last 20% of the Book of Ezekiel will be the locus of the visible Kingdom on earth.) The reader must note that the Christians in Thessalonica were not Jews, but Greeks living in Greece, and so when they feared the Day of the Lord had already started (2 Thess 2:1-2), they were not scared for themselves that the Romans were going to overrun Palestine anytime soon, but that the consummation of the Mystery had begun, and that the worldwide judgment of God (as later described in the Revelation of John) had already begun and they (the Thessalonian believers) were somehow "left behind."
So the "Times of the Gentiles" refers to the indefinite intercalary period of time on earth, which will one day end when the Lord comes back to earth to reestablish his rule and authority on the earth, when "the nations will be broken with a rod of iron and shattered like earthenware" (Ps 2:9 with Rev 2:26-27, Rev 12:5, and Rev 19:15). This havoc before the establishment of the visible kingdom will be the ultimate fulfillment of the words spoken by Jesus in Mark 13, Matt 24, and Luke 21 (and the words written by the Apostle John in the Book of Revelation, which was written after the fall of Jerusalem in AD 70).
In conclusion, Scripture points to the literal establishment of the theocratic kingdom on earth at some point in the future, which will be centered on the Temple described by Ezekiel (and which translates into the eternal Zionic Jerusalem described in Revelation 21:10-27, where the measuring rod appears again suggesting literal events and objects). And so, we can infer that the "Times of the Gentiles" is the period of time when the visible theocratic kingdom on earth is absent.