The mantra is a prayer to Lord Shiva who is addressed as Sankara and Trayambaka. Sankara is sana (blessings) and Kara (the Giver). Trayambaka is the three eyed one (where the third eye signifies the giver of knowledge, which destroys ignorance and releases us from the cycle of death and rebirth.
Namaste astu Bhagavan
Trayambakaya Tripurantakaya Trikalagni – Kalaya
Kalagni – Rudraya Nilakantaya Mrityunjayaya
Sriman Mahadevaya Namah
Meaning of Shiva Prarthana
I bow down to Lord Shiva
Who is the creator and protector of the universe, who is the greatest among gods
Who has three eyes, who is the annihilator of all the three worlds, one whose throat is blue, who is the conqueror of death
Who is the Lord of all, who is propitious
Who is possessed of all marks of greatness and who is the greatest among Gods.
To him my prostrations.