Amavasya is a Sanskrit word that means dark moon lunar phase. The dark moon tithi is when the moon is within the 12 degrees of angular distance between the sun and the moon before conjunction. On Amavasyas, Shraadh is done to forefathers by Bhramins whose fathers have died.
The Hindu calendar states that the first fortnight (15 days) of the month of Ashwin are considered very sacred for karmic cleansing and for performing rituals and prayers for the forefathers. Ashwin Amavasya is also known as Sarva Pitru Amavasya or Mahalaya Amavasya. These fifteen days are especially dedicated for those who intend to pray for the peace of their dead parents/grandparents/great grandparents etc. it is believed that performing rites and rituals during these days helps them attain peace, happiness and salvation for their forefathers.
Out of all the 15 days dedicated to pray for the forefather, sarva Pitru / Mahalaya/ Ashwin Amavasya holds utmost importance. Some even believe the full moon night of this month important to do the same, which is known as Pitra purnima. However in most of the parts of India, Ashwin/Sarv Pitra Amavasya is considered to be the most auspicious day to carry out Shraddh. There are stories behind why this day is called 'Sarva pitra amavasya' or ' Mahalaya Amavasya'. 'Maha' means great and 'laya' means devastation. It is believed that when divine nector (holy amrit) was being churned, the demons killed many saints and Devas, it happened on the Amavasya of the ashwin month. In India, we consider the holy people like saints and Devas as our ancestors and thus the last day of the Pitra Paksh is dedicated to them.
'Sarv' means all and pitra means forefathers/ancestors. Usually people perform ritual on the name of their forefathers on a specific tithi on which they died but at times, some of them do not know the specific tithi on which the mortal being of their ancestors left the body, in that case, 'Sarv pitra Amavasya comes to rescue. It is a day dedicated to all the forefathers irrespective of the tithi they died. The souls of our ancestors are bound with their karma they did on earth, and in order to provide them moksha(salvation), one needs to perform the rites and rituals of shraddh. One can also donate food, clothes, money on the name of their loved ones in order to expiate them of their karma.
Aswin Amavasya / sarv pitra Amavasya is considered to be the most auspicious and most powerful one for performing funeral rites and tarpan (libation of water).
Lord Ganesha is worshipped on this day as he is the God who helps in attaining peace, good health and moksha. Also he aids in removing all the obstacles in life. One must perform a ceremonial act for Lord Ganesha preferably with help of a well-versed pundit.