CALCULUS is the branch of mathematics dealing primarily with change. Calculus is the study of how things change. Calculus provides a framework for modelling of systems in which there are changes. It provides means for one to construct simple quantitative models of change and to deduce their consequences.
Before Newton and calculus, the study of the motions of the planets was at best limited to kinematics: you could observe the motions and try to describe them. As to what caused those motions, there could only be speculation.
Newton produced a dynamic theory: some simple physical laws that explained the motions as the result of the same forces that act on an apple falling from a tree. Moreover, with the mathematical techniques of calculus and differential equations (which is basically an extension of the calculus), the resulting motions could be calculated and predicted.
From that time on, most of physical science and engineering has been understood in terms of differential equations. The laws of physics give you differential equations that describe the rates of change of various quantities in a system you are interested in. By solving those differential equations, you can predict how the system changes as time goes on.
