Here is the context from Matthew:
(Matthew 24:29-31 NWT) . . ."Immediately after the tribulation of those days the sun will be darkened, and the moon will not give its light, and the stars will fall from heaven, and the powers of the heavens will be shaken. 30 And then the sign of the Son of man will appear in heaven, and then all the tribes of the earth will beat themselves in lamentation, and they will see the Son of man coming on the clouds of heaven with power and great glory. 31 And he will send forth his angels with a great trumpet sound, and they will gather his chosen ones together from the four winds, from one extremity of the heavens to their other extremity.
But breaking it down further:
Here is verse 29:
"Immediately after the tribulation of those days the sun will be darkened, and the moon will not give its light, and the stars will fall from heaven, and the powers of the heavens will be shaken.
Here is the parallel to Mt 24:29 in Luke:
(Luke 21:25, 26 NWT) . . .Also, there will be signs in sun and moon and stars, and on the earth anguish of nations, not knowing the way out because of the roaring of the sea and [its] agitation, 26 while men become faint out of fear and expectation of the things coming upon the inhabited earth; for the powers of the heavens will be shaken.
This portion, especially as brought out by Luke, relates action taking place among the gentiles.
The Jews had to deal with the prophecy related in Matthew 24:15 (when Gallus arrived to quell the Jewish rebellion [c. Nov 66] thru verse 22, thru the spring of 67 when Vespasian had started the Roman war against the Jews to destroy them, and on into 68 AD. This time was the beginning of "great tribulation" for the Jews. (Not just in Judea either. Jews all over the Roman empire were being assaulted as a show of support for the empire.)
Sometime in 68 AD Nero committed suicide and began what has been called, 'The Year of the Four Emperors.' Some references describe this roughly 18 month period as the greatest upheaval the Roman empire had ever seen up to that time. If the Roman Empire is taken as the figurative "heavens" (of Mt 24:29 and Luke 21:26), it was definitely "shaken." Fired cities all along the coasts, indeed, throughout the empire, left 'the sun darkened and the moon not giving its light' for many in the empire. Vespasian left his son Titus in charge of the Jewish War and brought order to the empire, he ending up as the fourth of the 'four emperors.'
It was following this that Titus made his seige of Jerusalem in 70 AD. Verse 30 of Mt 24, with its 'sign of the son of man' appears to be a reference to the final days of the Jewish rebellion and the destruction of Jerusalem. (See some discussion about it here and here. (See my posts 837, 839, 840 on the second link.)
If you take this prophecy in Mt 24 as directly foretelling what would happen to the Jews in the first century, then, verse 31 is describing the gathering of Christian "chosen ones" from the four corners of the earth. In other words, the Christian preaching work expands, historically, from this point out to the farthest reaches of the planet. Verse 31 is, in a few words, describing centuries of activity that would take place.
Verse 31, like 29 and 30, has verbal echos to a number of OT passages:
Deut 30:4 - 'gathering from one end of heaven to the other.'
Zech 2:10 LXX - similar to Deut 30:4
Isa 27:13 - great trumpet blast
Also compare Mt 24:31 with Mt 8:11-12
For angels doing the gathering - compare Mt 13:41 and 16:27, 25:31-34
The WT is mistaken in limiting the "chosen ones" to just the 144,000, although, they would be among those gathered. The WT assumes that only the 144,000 are "anointed." The NT never speaks of 'non-anointed' Christians. Receiving the "promised spirit" is part and parcel of what makes the New Covenant better than the Old Law Covenant. (Compare Galatians chapters 3 and 4)
Hope this is helpful (And sorry for the length of the post)
Take Care