A Tensor is a mathematical object for symbolic manipulation of relationships between other objects that belong in conceptually similar universes or spaces. Literature on Deep Learning, like Goodfellow, call for the CS-minded reader to just assume it's a fancy word for a matrix of more than two dimensions. That makes matters confusing because mathematically you could have scalar or vectorial tensors. The classic mathematical definition puts more restrictions on the "shape" of the "matrix" by requiring certain properties so that it can create a symbolic language for a tensor calculus. Then you can study how the relationships change as variables on the universes or spaces change.

Understanding the inertia tensor on classical mechanics or the stress tensor may illustrate where tensors come from, and I understand that GR also makes use of a lot of tensor calculus that came to be as mathematics developed manipulating and talking about tensors. I have a kinda firm grasp on some very rudimentary tensor calculus from trying to leanr GR, and a pretty solid grasp on classical mechanics. I've had hour long conversations with deep learning popes and thought leaders in varying states of mind and after that my understanding is that they use the word tensor in an overreaching fashion as like you could call a solar panel a nuclear fission reactor power source. This thought leaders include people with books and 1M+ view Youtube videos on the subject that use the word tensor and I'm not saying their names because they off-the-record admitted that it's a poor choice of term but it harms the ego of many Google engineers to publicly admit that.