Significance
The Bhishmaashtami vrat falls on the eighth day of the Magh Month's Shukla Paksha. The person, who performs the Tarpan for Bhishma with the seasome seeds on the Ashtami of Magh Shukla Paksha, gets the beautiful and talented child.
History
At the time of Mahabharata, Bhishma Pitamah was lying on the bed of arrows in the battle field and left his body only when Sun came into Uttarayana.
When Sun comes into Uttarayana, people who leave their bodies go directly to the Brahmalok (Heaven). On the Magh Shukla's Ashtami, Sun came in Uttarayana and then Bhishma Pitamah left his body as he was blessed with the boon of 'Iccha Mrityu' (death of wish).
And, that is how we commemorate the Death Anniversary of the Bhishma Pitamah.
How to Celebrate
On this day, everyone should do the Tarpan for Bhishma Pitamah. It is mentioned in Mahabharata, that the people who do the Tarpan for Bhishma Pitamah on this day are becoming free from all kinds of sins of the year:
Shuklashtamya Tu Maghasya Dadyaad Bhishmaay Yo Jalam|
Savatsarkritam Papam Tatchanadeva Nashyati||
While doing Tarpan, face towards South and do the Tarpan by following Mantra:
Vaiyaagrapadgotraay Saaskriyapravraay cha|
Gangaputraay Bhishmaay Sarvada Brahmcharine||
Bhishma Shantanvo Veerah Satyavaadi Jitendriyam|
Aabhiriddhirvaapnotu Putra Pautrochitaam Kriyaam||
Generally, people cannot do the Tarpan who have living parents, but on the day of Bhishmashtami they can also do the Tarpan for 'Bhishma'. This system has been started by Hemadri:
Maghe Maasi Sitashtamyaam Satilam Bhishmatarpanam|
Shraaddham Cha Ye Naraam Kryaste Syuam Santati Bhaginah||
It means, the person who perform the Tarpan for Bhishma with the seasome seeds on the Ashtami of Magh Shukla Paksha, gets the beautiful and talented child.