As is well known, Tolkien was a Roman Catholic. In Catholicism (as well as in other denominations) God is viewed threefold, being composed of the Father, Son and Holy Spirit. While the two former have clear purposes, the latter does not. It is in my view that Eru, being the supreme deity of Arda and Eä used the secret fire in a way Tolkien saw the Holy Spirit as. The secret fire is what gives living beings autonomy and is the source of all souls. In the Catholic view all souls originate with God as well, so it is my view that the secret fire is Middle Earth's reflection of the Holy Spirit. Please take what I said with a grain of salt, but I believe it is an interesting comparison. If anyone else has a different view I would love to hear it.