Tensor
A container of numbers with any number of axes; scalars, vectors and matrices are its rank 0, 1 and 2 cases.
In machine learning a tensor is simply an n-dimensional array, and its rank is how many axes it has. Rank 3 covers a batch of token sequences, shaped (batch, sequence, features). Rank 4 covers a batch of images, shaped (batch, height, width, channels).
The important property is that axes carry meaning your code assigns and the tensor does not record. A shape of (32, 10) cannot tell you which axis is the batch — that agreement exists only in your head, which is why every reduction has to be told which axis to act on, and why a wrong axis argument produces a different answer rather than an error.
Note that the machine learning usage is looser than the mathematical or physical one, where a tensor additionally has to transform in particular ways under a change of coordinates. Here it just means the array.