What is the significance of the anniversary of the death (known as yahrzeit, literally “year’s time”) of a parent?
TY for your Q, which touches on both philosophy and practice (albeit not strictly speaking in the realm of halakhah, Jewish Law). Philosophically, the concept of yahrzeit reflects our belief in the immortality of the soul, ie the essence of a person which lives on in the next world. Although it is uncertain if the passing of time has the same significance in the World of the Souls as it has for us, the yahrzeit is an opportunity to recall and honour the memory of the deceased.
WRT how the yahrzeit should be marked/observed, time-honoured tradition stipulates the lighting of a candle to burn throughout the 24 hours, and (for a son or sometimes other relative) to recite kaddish and to lead the prayers in shul on that day. Torah study and tzedakah in memory of the deceased is also very much appropriate. The classic sources mention the tradition of fasting on the yahrzeit as well. However this is no longer common practice in Ashkenazic circles, and particularly not among Hassidim. Rather, providing food and drink for friends (or even strangers) is considered a greater source of merit, as the blessings recited on the food and drink accrue to the merit of the deceased. This is known as a “tikun”, ie corrective to the soul in the Next World. This is also the source of the tradition of sponsoring the Kiddush on the Shabbat before (or in the vicinity of) the yahrzeit.
Rabbi Rashi Simon