Thai is the first Solar month in the period of Uttarayana according to the Tamizh calendar. The complete month of Thai is therefore considered an auspicious month.

Thai Pusam is the day Pusam or Pushya Nakshatra presides in this month, It also mostly coincides with the full moon day or Purnima of this month. It is on this day that Parvati Devi is said to have gifted Her son Sri Karthikeya the divine lance “Vel”, in order to destroy the asura brothers namely, Sura Padma, Simha Mukha, Tarakasura and their army including a cousin Kraunchasura.

Shad- anana means six faced. Karthikeya is said to have 6 faces and is also referred to as Shanmukha. This Stotram is recited by Sage Agastya in praise of Sri Karthikeya in Skanda Purana, one of the 18 Mahapuranas.

Karthikeya is the favoured deity in the Southern States of India in Tamil Nadu, Kerala and Karnataka. This festival is celebrated with great fervour by Tamizhs all around the world.

Ref:

https://www.vedadhara.com/shadanana-ashtaka-stotram-lyrics

Chinmaya Sarveshwara: YouTube.com/watch?v=Ws-AyA1ZFhA&t-1529 for meanings in Tamizh.