There are quantities used in physics for which the concept of a number or a vector is insufficient. A more general notion of a geometrical object was required. The number (scalar) and vector were defined as tensors of a lower "rank" and then tensors of higher rank were defined. Two such tensos come to mind. The tidal force tenso which are found herechandran said:why the concept of tensor was invented. I always see that tensors are provided in matrix format. example inertia tensor is there in a 3x3 matrix.