Newton's laws, discovered more than 300 years ago, describe the motion of all objects that are not too fast, small, or heavy. The discovery of Newton's laws signalled the beginning of physics as a truly predictive science.
Newton's second law is a second order differential equation${}^\dagger$, \begin{equation*} \frac{d^2{\bf x}}{dt^2} = \frac{{\bf F}}{m}.\tag{1} \end{equation*} In words, the second derivative of the position of an object with respect to time, the acceleration, is directly proportional to the net force impressed upon the object, and inversely proportional to the mass of the object. Without calculus and the machinery of differential equations, (1) is one of nature's incomprehensible secrets.
Given the object's initial position and velocity, Newton's laws can be used to predict its subsequent motion. If the initial conditions and the forces are known with great certainty this prediction will describe everything about the motion of the object far into the future.
Every day countless physicists and engineers rely on Newton's laws to find out where the artillery round will land, how will the car crumple on impact, whether the bridge will fall down in a strong wind, and so on.
${}^\dagger$Differential equations relate derivatives of a function to the function itself.