Pitri Paksha

--> Pitru Paksha , also spelt as Pitru paksha or Pitri paksha, - literally translated to  "fortnight of the ancestors"

 is a 16–lunar day period in Hindu calendar when Hindus pay homage to their ancestor(Pitrs), especially through food offerings.
 The period is also known as Pitru Pakshya, Pitri Pokkho,Sola Shraddha , Jitiya, Mahalaya Paksha and Apara paksha.

Legand:
 

According to Hinduism, the souls of three preceding generations of one's ancestor reside in Pitru–loka, a realm between heaven and earth. This realm is governed by Yama, the god of death, who takes the soul of a dying man from earth to Pitru–loka. When a person of the next generation dies, the first generation shifts to heaven and unites with God, so Shraddha offerings are not given. 

Thus, only the three generations in Pitru–lokaare given Shraddha rites, in which Yama plays a significant role.According to the sacred Hindu epics, at the beginning of Pitru Paksha, the sun enters the zodiac sign of Libra (Tula). Coinciding with this moment, it is believed that the spirits leave Pitru–loka and reside in their descendants' homes for a month until the sun enters the next zodiac—Scorpio (Vrichchhika)—and there is a full moon. Hindus are expected to propitiate the ancestors in the first half, during the dark fortnight.

When the legendary donor Karna died in the epic Mahabharata war, his soul transcended to heaven, where he was offered gold and jewels as food. However, Karna needed real food to eat and asked Indra, the lord of heaven, the reason for serving gold as food. Indra told Karna that he had donated gold all his life, but had never donated food to his ancestors in Shraddha. Karna said that since he was unaware of his ancestors, he never donated anything in their memory. To make amends, Karna was permitted to return to earth for a 15–day period, so that he could perform Shraddha and donate food and water in their memory. This period is now known as Pitru Paksha.In some legends, Yama replaces Indr^a.

Significance

The performance of Shraddha by a son during Pitru Paksha is regarded as compulsory by Hindus, to ensure that the soul of the ancestor goes to heaven. In this context, the scripture Garuda Purana says, "there is no salvation for a man without a son". The scriptures preach that a householder should propitiate ancestors (Pitris), along with the gods (devas), ghosts (bhutas) and guests. The scriptureMarkandeya Purana says that if the ancestors are content with the shraddhas, they will bestow health, wealth, knowledge and longevity, and ultimately heaven and salvation (moksha) upon the performer.

The performance of Sarvapitri amavasya rites can also compensate a forgotten or neglected annual Shraddha ceremony, which should ideally coincide with the death anniversary of the deceased. According to Sharma, the ceremony is central to the concept of lineages. Shraddha involves oblations to three preceding generations—by reciting their names—as well as to the mythical lineage ancestor (gotra). A person thus gets to know the names of six generations (three preceding generation, his own and two succeeding generations—his sons and grandsons) in his life, reaffirming lineage ties. 

 Anthropologist Usha Menon of Drexel University presents a similar idea—that Pitru Paksha emphasises the fact that the ancestors and the current generation and their next unborn generation are connected by blood ties. The current generation repays their debt to the ancestors in the Pitru Paksha. This debt is considered of utmost importance along with a person's debt to his gurus and his parents.