The 6th lunar day known as Shashti is very auspicious for Lord Murugan who is also known as Skanda or Kandha or Kartikeya. HE is the warrior God who protects the devas.
In the Tamil month of Karthigai the 6th waxing lunar day is extremely powerful and is celebrated as Skanda Shashti. Devotees observe a 6 day fast starting from the 1st lunar day in the month of Karthigai.
According to Skanda Purana, there were 3 asuras (demons) in the name of Soorapadman, Singamugasuran, and Tarakasur who caused great troubles to the Gods. So Lord Kartikeya was created from the third eye of Lord Shiva to fight them. Lord Kartikeya was blessed with a spear weapon (vel) from Goddess Parvati.
The war took place in a place called Tiruchendur. During the war, Lord Kartikeya transformed Singhamugasuran as a vehicle of Goddess Shakti.
Soorapadman tried to disguise himself as a mango tree in the seabed. Lord Kartikeya split the mango tree into 2 halves. One became the Peacock which is the vehicle of Lord Kartikeya and the other half became the rooster which appears in the flag or banner held by Lord Kartikeya.
The destruction of the three asuras symbolizes the destruction of Ego, Pride, and Illusion.