The fortnight (15 days) preceding the Dasara or Navaratri is known as Mahalaya Paksha or Pithru Paksha. This period is important for honoring our ancestors. Men, whose fathers or Mothers have passed away, offer their obeisance (shraddha) to their ancestors during this period.
The last day of this period called as Mahalaya Amavasya, the new moon day, is considered as the most important day in the year for performing obsequies and rites.
This year in the Khara Nama Samvatsara, Mahalaya Amavasya falls on September 27th 2011. The pitru tarpana given during this time is a way of showing gratitude to your departed ancestors.