Tensors are necessary in order to express the curved geometry of spacetime. Without tensors, physics would be limited to linear equations, which don't describe the curved nature of spacetime very accurately. Tensors also play a fundamental role in the theory of general relativity, and are necessary for describing the forces between masses (gravity) as well as the behavior of light. In fact, many of the most important results of general relativity can only be derived using tensor calculus.