What is a Tensor?
A tensor is a mathematical object that has indices and and components.
Tensors are a generalization of math objects such as scalars and vectors. A scalar is a zero rank tensor and a vector is a first rank tensor. The rank describes the dimensionality of the scalar.
The rank of a tensor can also be thought of as the amount of indices required to access its components. A rank 2 tensor has rows and columns, and therefore requires 2 indices to access.