According to Mahabharat, when Kunti’s first son, Karna died; he because of his deeds went to heaven where he was offered precious stones and gold by Indra Dev. To this, Karna wished to have Food and Water, not these jewels. However, Indra Dev told him that he will be getting only those things that he had been donating in the name of his ancestors when he was alive.
Then, Karna explained to Indra that he had no idea about his ancestors as he was blessed by Surya Dev. After this discussion, Karna was sent back to earth for 15 days to donate Food and Water in the name of his ancestors. That is how a 15 day period came into existence and is named Pitra Paksha; in addition to this, the things donated during this period are called Shraadh.