Linearity is an extremely useful property of equations in physics. If an equation is linear, it allows you to easily add together simple contributions from individual elements to get a solution for a more complex situation. One example of a simple linear equation in classical mechanics is F = ma. If you find the individual accelerations of a particular body due to various individual forces, you can then add those accelerations to find the acceleration due to all of the forces acting together. If Newton's second law were not linear, introductory physics would be a much more difficult and confusing subject!