From the start of Elul through Rosh Hashanah, Yom Kippur, and into Sukkot, the custom is to say Psalm 27 LeDovid Hashem Ori Veyishi, a psalm of David: “The Lord is my light and my salvation.” 
And the traditional explanation that's given is that there is a sort of coded reference to Rosh Hashanah, Yom Kippur, and Sukkot in the psalm itself.
The rabbi said in Vayikrah Rabbah, “The Lord is my light on Rosh Hashanah, my salvation on Yom Kippur,” and “ki yitzpeneini besukko”: “He will shelter me or hide me in His sukkah” refers to Sukkot.
However, there was a difference of customs. Some people did not say it during Sukkot. Some people only said it up to and including Yom Kippur.
And there is, in particular, a disagreement as to whether you say or you don't say it on Shemini Atzeret. Do you stop on Hashana Rabbah or do you say it on Shemini Atzeret and stop then?
This led to an extraordinary case, one of the most remarkable in Anglo-Jewish history, decades ago before I was born. It happened in one synagogue in London that the chazzan on Shemini Atzeret began saying LeDovid Hashem Ori Veyishi.
The warden said, “Sha!” The chazzan [cantor] kept going. The warden said, “You don't say LeDovid Hashem Ori Veyishi on Shemini Atzeret.” The chazzan said, “You do.” The warden said, “You don't!”
The chazzan said, “But I'm the chazzan.” And the warden then said, “But I'm the warden. You're fired.” And he sacked him on the spot.
When Yom Tov was over, the chazzan took his case to an English civil court on grounds of unfair dismissal. The case came before a non-Jewish judge, obviously.
And he had to rule whether the chazzan had been dismissed with cause or without cause, which in turn depended on the question, “Do you or don't you say LeDovid Hashem Ori Veyishi on Shemini Atzeret?”
How was the judge supposed to know? How is he supposed to rule on something that is in fact an argument in Jewish law? The judge did something absolutely brilliant. He had the psalm read out, in full, in English, in court.
And then he turned to the litigants and said, “That psalm is so beautiful that I think it should be said every day.” The chazzan got his job back, and peace and order was restored. It's a lovely story.
And then he turned to the litigants and said, “That psalm is so beautiful that I think it should be said every day.” The chazzan got his job back, and peace and order was restored. It's a lovely story.
And that perhaps is why we say it at these times of judgement. Listen to how it begins. “The Lord is my light and my salvation, whom then shall I fear?
The Lord is the stronghold of my life, of whom then shall I be afraid?” And it ends with these words: “Hope in the Lord be strong, and of good courage in hope in the Lord.”
And that I think is what it's all about. On these difficult days, in which our lives pass in judgement on Rosh Hashanah and Yom Kippur, in which we leave the security of our homes and sit exposed to the elements on Sukkot...
...Psalm 27 perfectly expresses our faith that God is sheltering us from harm and that nothing can make us afraid.
