If God has made the world a perfect mechanism, He has at least conceded so much to our imperfect intellect that in order to predict little parts of it, we need not solve innumerable differential equations, but can use dice with fair success.

This quote is referring to the fact that although God has created the world to function perfectly, He has given humans an easier way to predict and understand certain aspects of it than having to solve difficult equations. He has given us the ability to use simple dice to make fairly accurate predictions about certain elements of the world around us.