During Mahalaya Amavasya, people offer prayers to their ancestors at early dawn. The ritual is called Shraddh or Tarpan.
Devi Paksha falls in the Ashwin month (September-October) when the moon is waxing, according to the traditional Hindu Lunar calender. It is believed that Mother Durga begins Her journey to the earth on Devi Paksha. The idols of Mother Durga gets ready for Durga Puja during Devipaksha. It is to be noted that Mother Durga's (Durga statue) eyes are drawn on the Mahalaya, which is called 'Chakshu Daan'. Mahalaya and Devi Paksha set the fervent mood for Durga Puja. It is the day when people roll up their sleeves to take up the preparatory measures necessary for Durga Puja.
Durga Puja in the beginning was observed during the month of Chaitra or the spring season during Basant Panchami. However with Lord Rama worshipping Mother Durga during the Autumn season to seek Her blessings just before His battle with Ravana, Durga Puja came to be observed during this season. Hence the festival also acquired the name 'Akhaal Bodhan' or 'Untimely welcome' owing to the untimely welcome of Mother Goddess.
Devi Paksha falling on Mahalaya is a reminder to prepare one for the subjugation of the ego during Durga Puja. It instills the spirit of surrender with its preparatory means, to offer one self to Mother Durga for the final destruction of the ego. The Mother simply strikes the ego of the surrendered soul to bless with the bounty of eternal bliss of self realisation.
Lets us thus surrender to the Mother to realise the bliss of the being.