First of all, there are some in the Prophecy circle who believe that the Rapture will occur during the Feast of Trumpets, a Jewish Feast, and it was implemented as a time of preparation for the Day of Atonement, it was a time of prayer and repentance and was done some days prior to The Day of Atonement that would be when the High Priest would make a sacrifice for the atonement of sins
Without going in depth about Jesus fulfilling the Feasts, I can just say that the Feasts have nothing to do with The Church, but with Jesus himself.
Some believe the Rapture will occur during the Feast of Trumpets because of the mention of the sound of the trumpet of God at the time of the Rapture.
There's no scripture to give details on the actual significance of this but some commentators say that the sound of the trumpet could be a literal trumpet sound, like that of the Shofar, since they were used to call for the assembly of God's people, and to announce the coming of The King, and such.
But others say it could be The actual voice of God that is heard which is consistent with some scriptures like
"I was in the Spirit on the Lord’s Day, and I heard behind me a loud voice, as of a trumpet,"
Revelation 1:10
"And when the blast of the trumpet sounded long and became louder and louder, Moses spoke, and God answered him by voice "
Exodus 19:19
"...to a trumpet blast or to such a voice speaking words that those who heard it begged that no further word be spoken to them"
Hebrews 12:19
I think the importance here is to be careful not to get caught up in associating the Rapture with a Feast day because then comes the tendency to get into date setting and that can lead to disappointment when those feast days come and go.
The Rapture of the church is imminent and has no signs or dates associated with it.
We just watch and wait and be ready for Jesus appearing
Also we know that the Church age dispensation has nothing to do with the Jewish dispensation that resumes after the Rapture when God turns His attention back to Israel.
I'm just throwing this out there from what I have learned about the topic of Feast days and the significance of the trumpet sound that could very well be The Lord's voice saying
"Come up here" as he did with John when he took him up in the spirit when John was given the Revelation of Jesus Christ.
Open for discussion if anyone has a comment about this.