Great question! In order to answer that, we must back up to Luke 21:10-19 where we see Yeshua talking about people fighting, nations at war, etc. - because, as you know, satan has already been in control of the earth (gentiles/heathens/pagans) since the beginning. We know this because in Luke 4:5-7, satan is offering the earth to Yeshua, to follow him! Of course, Yeshua doesn't; and, instead of fighting and arguing with the devil, He quotes Torah and says to worship YHWH only.
And so, in verse 21-24, the "times of the Gentiles be fulfilled", or "fullness of the Gentiles" means that satan's control of the gentiles will come to an end, and people will have to make a choice between him and YHWH.
Luke 21: 10. For nation will rise against nation and kingdom against kingdom. 11. And there will be severe earthquakes from place to place and famine and plagues. And there will be fears and terrors and great signs will be seen from Heaven. And the winters will be severe. 12. But before these things, they will lay hands upon you and persecute you. And they will deliver you to the assemblies and to the prisons. And they will bring you before kings and governors because of my name. 13. But it will be to you for a testimony. 14. But place it in your hearts that you should not try to learn how to answer. 15. For I will give you a mouth and wisdom so that all your enemies will not be able to stand against it. 16. And your parents and your brothers and your relatives and your friends will betray you. And they will kill some of you. 17. Then you will be hated by all men because of my name. 18. Yet not a strand of hair from your head will perish. 19. And by your patience you will gain your souls.
Luke 21: 20. And when you see that an army has surrounded Urishlim, then know that its destruction has drawn near to it. 21. Then those who are in Yehuda, let them flee to the mountains. And those who are within it, let them flee. And those in the villages, let them not enter into it. 22. Because these are the days of vengeance that might be fulfilled everything that is written. 23. But woe to those who are pregnant and to those who are nursing in those days! For there will be great distress in the land and wrath upon this people. 24. And they will fall by the edge of the sword and be led away to every land. And Urishlim will be trampled by the Gentiles until the times of the Gentiles be fulfilled.