Aadi Amavasya, ancestor worship in Hindu culture

New Moon day. Aadi Amavasya gansripar.blogspot.com

Aadi Amavasya, Ujjain. drikpanchang.com

The practise of Aadi Amavasya virutham (fasting) and doing tharpanam on that day has been in the Hindu culture for several centuries. Even in Christianity, there is a simple ritual every year and on that day  devout Christians visit the tomb of their ancestors in the church graveyard and light candles or place flowers on the slab.  What does the Bible say about ancestor worship?  According to the Bible  the spirits of the dead go to either heaven or hell and do not remain in the natural world (Luke 16:20-31; 2 Corinthians 5:6-10; Hebrews 9:27; Revelation 20:11-15). The belief that spirits continue to reside on earth after death and influence the lives of others is not scriptural.

The Day of the Dead, Mexicao. learnreligions.com

The Day of the Dead is celebrated on November 1 by  Mexicans and  many Mexican communities in the US. On this occasion  ''families gather together, pack picnic lunches, and go to cemeteries to honor the memories of family members who have died in 
the past year. Altars include colored tissue ribbons, flowers,
photos of the dead, and candles. It's also popular to include food offerings with a theme of death - sugar skulls and coffins 
are a common item, as are small figures made of bread'' (https://www.learnreligions.com/ancestor-worship-in-pagan-cultures-2562898)
Aadi Amavasya (new moon day)  that comes in the month of Aadi (August)  as per Tamil calender is an auspicious day for the Hindus across India. It  has different names - Haryali or Shravan Amavasya in the northern India, Ashada Amavaya as per  Telugu, Kannada and Marati calenders. Also it is known as Chukkla Amavasya in Andhra and Bheemana Amavasya in Karnataka. 

New Moon day. Aadi Amavasya riyial, pondicherryarun.com

Ancestor worship is focused on  religious beliefs and practices consisting of prayers and offerings to the spirits of dead relatives. It is  in many cultures all across the world.  Normally, prayers and offerings are made because it’s believed the spirits of ancestors live on in the natural world and are thus able to influence the futures and fortunes of the living relatives.  Further, they are  believed to influence the lives of later generations by blessing or cursing them, in a sense acting as  gods. So praying to them, presenting them with gifts, and making offerings are done  once a year to appease them and gain their favor.

In many cultures ''death'' alone was not a criterion for being worshipped as an ancestor. It is essential the  person must have lived a blemish-less  moral life with great social distinction in order to attain that status and stand apart. In some cultures ancestors’ spirits are also believed to act as mediators between the living and the Creator. The Christianity does not believe in medium, etc. 

Did ancestor worship exist before Christ?  Evidences found at sites in the Near East in Jericho  point out  that such a worship did exist in  the 7th century before Christ. It existed in ancient Greek and Roman cultures as well.  This kind of worship has influenced  Chinese and African religions and also Japanese and Native American religions. So ancestor reverence is universal and is not unique to the ancient  Indian culture.

On this day, Hindus in millions perform  ''Pithru karyam'' on the banks of sacred river like the Cauvery, Krishna, ,Godhavari, Ganga, etc and people go to  Agni Thertham, Rameswaram where they do this ritual on the seashore. The rituals include simple 'thithi' or 'tharpanam' invoking blessings from the forefathers and dead ancestors.  Amavasya is a sort of thanks giving  ritual dedicated to the ancestors.  Yesterday  July 31, being the Aadi Ammavaya day, lots of people went to Thiruvaiyaru which is about 7 miles from my native town and did tharpanam, etc on the banks of the Cauvery. They bathe in the rives or in the sea before the ritual. By performing this ritual, they remember, with reverence,  their departed forefathers and do obeisance to them. The belief is the forefathers bless their descendants with prosperity, good health and welfare. Invariably, countless people do thithi guided by the priests/ pundits.  Agni Theertham in Rameswaram, Thriveni Sangamam in Kanyakumari, confluence of the Cauvery near Erode, Srirangam. Kumbakonam  and Thiruvaiyary near Thanjavur are important holy therthams in Tamil Nadu.  

Aadi is an important month for the temples dedicated to Karthikaya/ God Muruga. On this day, special abhishekams and pujas are held done to the main deity and at Palani, TN devotees of Muruga never fail to bathe  in the Shanmuga River.

Amavasai is believed to be spiritually and, from health point of view,  beneficial and most of the devout Hindus will be content with just one meal preferably before noon.  On this day our  forefathers/ancestors are, said  to descend from their abode of 'Pitru Loka'/Ancestral World, to the earth during these times of the year. If you do pithru karyam, it will please them  and they will help us tide over our day to day problems and give us mental strength to tackle them with confidence. 

The most effective way to communicate with them is invocation by chanting mantras and performing  'Tharpanam' or 'Shraartham' with utter dedication. The pindam in the ritual is equal to feeding our ancestors with annam - food. Donating clothes, etc feeding the cows with fruits and vegetables is a nice way to express our gratitude to our forefathers. Yet another benefit is spiritual rejuvenation which is essential for our prowess.  
https://www.gotquestions.org/ancestor-worship.html
https://www.hindu-blog.com/2009/07/aadi-amavasya-2009-amavasi-or-no-moon.html