Sarvapitri Amavasya is the last day of Pitru Paksha, also spelled as Pitri Paksha. For the uninitiated, Pitru Paksha is a 16-lunar day period when Hindus pay homage to their ancestors through shradh prayers and food offerings. The period falls in the lunar month of Bhadrapada beginning on the full moon day or the day after full moon day. It is believed that performing rites helps liberate souls to attain salvation from the vicious circle of life and death. The period is considered inauspicious, given the death rite performed during the ceremony, known as shraddh or tarpan. Pitru Paksha is also known as Pitri Pokkho, Sola Shraddha, Apara Paksha, and Mahalaya Paksha.

Sarvapitri Amavasya is the most important day of Pitru Paksha. Those who have forgotten to perform shraddh can do the same on this day. It is believed that shraddh ritual performed on this day is considered fruitful. If you are unaware of the death tithi of ancestors, their shraddh ritual is advised to perform on Sarvapitri Amavasya. In 2018, Sarvapitri Amavasya begins on October 8 and ends the next day.

In Hindus, it is believed that one suffers the loss of wealth, failure in life and business if ancestors are not happy. During pitru paksha, the soul of the departed ancestors is believed to visit the family’s house. After being satisfied with puja rituals and food offerings, the soul blesses their descendants and return back.

Significance
As per Hinduism, the souls of three preceding generations reside in Pitru-loka, a realm between heaven and earth. The realm is looked after by Yama, the god of death. It is believed that when a person of the next generation dies, the first generation shifts to heaven and unites with the God. Only the three generations in Pitru-loka are given Shraddha rites.

Legend
When Karna, the great warrior from the Hindu epic Mahabharata, died during the war his soul transcended to heaven. Karna was offered gold and jewel as food but he needed real food to eat. He approached Lord Indra and asked the reason he was served gold as food (In some legends Yama replaces Indra). Indra revealed that Karna has donated gold all his life but had never donated food to his ancestors. To which Karna replied that he was unaware of the ritual and his ancestors. To control the damages, Karna was allowed to visit earth for a fortnight so that he could perform the death rituals of his ancestors and donate food and water. This period is known as Pitru Paksha.

Tithi
Amavasya tithi begins: 11:31 am on October 8
Amavasya tithi ends: 9:16 am on October 9

Source: http://www.freepressjournal.in/webspecial/sarvapitri-amavasya-2018-significance-of-the-last-day-of-pitru-paksha/1370671