Fundamentally tensors are very much like vectors. The idea is stolen from physics. Imagine pushing a box on a two-dimensional plane. If you push the box with a force of 1 Newton along the x axis, there is no force applied to the y axis. You would write the vector as such: [1, 0]. If the box were moving along the x axis with at a speed of 10 km/h and along the y axis with a speed of 2 km/h, you would write the vector as such: [10, 2]. Note that they are unitless: the first example was a vector of Newtons, the second example was a vector with km/h as its units.
In short, it is a representation of something (a force, a speed, or anything with magnitude and direction) applied to a direction. From this idea, computer science ...