Because that is when their holy ruach (spirit) hovers and rests on their grave to bring salvations to those who daven there and seek Hashem's compassion.
The person saw the stone, he was immediately healed. When Avraham was niftar, Hakadosh Baruch Hu hung the stone in the sun." The Rashba (quoted in Ein Yaakov) explains that the "good stone" on Avraham's neck refers to Avraham's voice. With his voice, he brought many people to the true emunah." The Minchas Yitzchak (Drashos p.199) adds that this stone, which hung from Avraham's throat, also alludes to Avraham's tefillos. His voice of tefillah healed people and saved them. Regardless of whether they needed a refuah or spiritual healing, Avraham had that "Special stone in his throat," which means he had the power of tefillah.
When Avraham was niftar, Hashem placed this stone in the sun. The Minchas Yitzchak explains that the sun returns once every year to the place where it began, and also a tzaddik, on the day of his yahrtzeit, when people daven at his kever, they can have their salvation. Whether they suffer spiritual or physical ailments, they can have their salvation. The Minchas Yitzchak adds that when we can't go to the kever, we can also attain yeshuos "when we gather in his honor."
12. Rebbe Yissachar Dov of Belz zt'l explained that when a tzaddik goes to heaven, looks down, and sees the suffering in this world, he understands very clearly how everything we go through is all for our benefit. From his viewpoint in heaven, he sees everything in a much more positive light. As it is told about the Rebbe Reb Elimelech of Lizhensk zt'l, he said to his student, Rebbe Mendel of Riminov zt'l, that he promises that when he is niftar, he will annul a particular decree that was then on the Jewish people. Time passed, and Rebbe Elimelech came in a dream to Rebbe Mendel of Riminov and said, "Now that I am in heaven, I don't see that the decree is bad anymore. Every decree is good. So how can I annul it?" But on the yahrtzeit, the tzaddik comes down to this world, and then he can see and perceive the great tzaros we endure in the way we experience them. When this occurs, he is motivated to annul all the harsh decrees and to daven for salvations for Bnei Yisrael. This is why the yahrtzeit is called hilulah, an expression of joy. There is a lot of joy and salvations on this day because the tzaddik understands our tzaros and prays for our salvation.
The Gemara (Pesachim 51.) states, "Rav Yosef, the son of Reb Yehoshua ben Levi, became ill and was niftar (and then he came back to life). When he returned to this world, his father asked him, 'What did you see in heaven?' He replied, 'I saw an upside-down world. Those above [in this world] are below [in heaven], and those below here are above there. His father told him, 'You saw a true world.'" On a yahrtzeit, when those who are above come below to this world, that is a time when the people of this world below can go above. This means we can live better, as if we are in heaven and everything becomes good.
The Sifri (Eikev 38) teaches, "Tzaddikim bring blessings wherever they go. When Yaakov came to Lavan, he brought blessings... When Yosef came to Potiphar, he brought blessings... Yaakov came to Pharoah and brought blessings because the hunger ended before its time..."
The Sifri then discusses whether a salvation from a tzaddik is eternal. The Sifri writes, "After Yaakov was niftar... the hunger returned. Reb Shimon Bar Yochai said, 'This isn't a kiddush Hashem. The words of tzaddikim exist when they are alive and don't cease after they are niftar. The bounty that comes from a tzaddik is eternal, forever." Based on the above, we can be certain that the tzaddikim continue to perform miracles after their passing, as they performed miracles when they were alive. Many brachos come to the Jewish nation in the merit of tzaddikim.
עולמים תשועת 'בה נושע ישראל, "Yisrael receives their salvations from Hashem, an eternal salvation." The roshei teivos spell עין בת. This is a hint that salvations will come to the Jewish nation on the Bas Ayin's yahrtzeit. Also (Tehillim 34:3) states, וישמחו ענוים ישמעו נפשי תתהלל 'בה, "My soul boasts of Hashem; may the humble hear and rejoice." The roshei teivos spell עין בת.
Yismach Yisrael (Me'oron shel Yisrael 14 Shevat 2) says that the yahrtzeit is called הלולא because, in Aramaic, a chasunah is also called hilulah. The celebration of a yahrtzeit is compared to the joy of a chasunah. And just like at a chasunah, the kesubah is read before the chosson to remind him of his obligations to the kallah, so too, on the day of the hilulah of a tzaddik, the tzaddik is reminded of his obligations to the people who are בצלו החוסים reside under his shade (which means those who are students of this great tzaddik).
And this doesn't mean solely those who were the tzaddik's students when he was alive; it includes those who try to go in this tzaddik's ways and learn from his divrei Torah after his passing. If someone living in our times in the year, ה"תשפ, desires to learn from the ways of the tzaddik and wants to study his divrei Torah, he can be called בצלו החוסים, 'under the shade' and a student of this great tzaddik. On the day of the hilulah, when the tzaddik is reminded of his obligations to help those who are under his shade (בצילו החוסים) this certainly also includes the new students, who didn't know the tzaddik. Perhaps they didn't even see the tzaddik when he was alive, but they seek to learn from this tzaddik and to become influenced by his ways and from his divrei Torah.
