It is very difficult to know for sure why any particular religious belief comes to be prominent at a given time. However, we can speculate that deism came about because of the advances in science and the changes in people's views of the world that came along with the Enlightenment.
The Enlightenment made people start to think about the world in a more rational and scientific way. Science came to be able to explain more and more things and fewer things were mysterious. In such a situation, it is perhaps understandable that people started to think in a rational manner about God.
Deism is something of a compromise between traditional religion and pure rationality. It does not go so far as to deny the existence of God, but it does say that God does not interfere in the world, doing things like breaking the established scientific laws that govern the universe. We can surmise that such a belief came about because of scientific advances that made the world seem more understandable and logical.