This is a great question since the little verse found below seems to be inexplicable without it.
7And the word of God increased; and the number of the disciples multiplied in Jerusalem greatly; and a great company of the priests were obedient to the faith. The priests, who performed the temple service knew how the thick curtain which separated the Most Holy Place, where God's presence was said to dwell (though they of course also believed that the most high does not just dwell in temple's made with human hands) from the Holy Place - they clearly knew, since that was their particular and special occupation, how no-one would dare, or even could enter that place except the High Priest, once a year, to make atonement for the people. The priest also knew that no mortal could tear that curtain -it was so thick and strong.
The fact that a great many of them believed verifies the fact, to those who wish to ponder it a little while, hidden from the general public, of what went on at the time when Jesus died.
The Gospel record seems to suggest that this was at the precise moment when Jesus died.
50Jesus, when he had cried again with a loud voice, yielded up the ghost. 51And, behold, the veil of the temple was rent in twain from the top to the bottom; and the earth did quake, and the rocks rent; This of course is particularly mentioned in Matthew (since he wrote for the Jews and highlighted things of interest to them which would have required long and detailed explanations for Gentiles). He does not state it explicitly either, possibly due to a reverence for the divine name, but it is clear that this was a supernatural event and could have only been performed by the hand of almighty God -not just in terms of strength (much less than almightiness being required here), but in terms of who did it. No Jew, not even the high priest himself would dare to perform such an act were they able.
The tearing of the Temple curtain was an emphatic statement that the separation between God and a Holy God was at an end and that such symbolic acts as performed by the High Priest were no longer necessary, since Christ the ultimate passover Lamb had been slain to atone for the sins of the whole world and to thereby open the way to God and His presence. The curtain really symbolized the great separation that must exist between man and a God who is perfect in all His ways and in His very nature. Such was now done away with by the finished work of Jesus Christ on the cross. Those priests who were 'on duty' at the time of course knew about this first, and the evidence was before the rest as the terrible news spread, as would have the realization of when it happened. All this explaining the testimony of Acts 6:7. In summary, the tearing of the temple curtain was done by almighty God, who saw the finished work of His son on the cross and was satisfied.