One legal definition of an Act of God (from Black's Law Dictionary): An act occasioned exclusively by violence of nature without the interference of any human agency.
I think the history of the term is straightforward. The English common law was grounded in old-fashioned Calvinism. Any act that has no human intervention must come from God's providence. This was plainly acknowledged.
The significance of it as a legal term is that the law does not impute responsibility to a party if the damage complained of was not caused by any person.
So, in the insurance world it is a term of art, and it is always spelled with and "o."