The Secret Fire, seems to refer to that aspect of Eru Ilúvatar which is his Power of Creation. It was with Ilúvatar at the beginning, and later Ilúvatar set it (or an aspect of it) at the centre of Arda.
- "Therefore Ilúvatar gave to their vision Being, and set it amid the Void, and the Secret Fire was sent to burn at the heart of the World; and it was called Eä."
- ― Valaquenta, the Silmarillion
The Secret Fire is also described as being part of all feä: it is that Gift which makes sentient beings capable of independent thought.
- "You cannot pass, I am a servant of the Secret Fire, wielder of the flame of Anor. You cannot pass."
- ― The Fellowship of the Ring, The Bridge of Khazad-dûm
Loosely, it could be taken as an alternate name of the Holy Spirit.